17Cxx Jordan structures
This subtopic studies Jordan structures, including Jordan algebras and triple systems, with attention to structure theory and applications in analysis and geometry.
Specific topics
17C05 Identities and free Jordan structures
Overview
17C05 studies general jordan algebras in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
General Jordan algebras (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for general jordan algebras
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks
17C10 Structure theory for Jordan algebras
Overview
17C10 studies special jordan algebras in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
Special Jordan algebras (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for special jordan algebras
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks
17C17 Radicals in Jordan algebras
Overview
17C17 studies jordan pairs and triple systems in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
Jordan pairs and triple systems (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for jordan pairs and triple systems
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks
17C20 Simple, semisimple Jordan algebras
Overview
17C20 studies jordan structures from associative algebras in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
Jordan structures from associative algebras (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for jordan structures from associative algebras
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks
17C27 Idempotents, Peirce decompositions
Overview
17C27 studies jordan homomorphisms and identities in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
Jordan homomorphisms and identities (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for jordan homomorphisms and identities
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks
17C30 Associated groups, automorphisms
Overview
17C30 studies jordan algebras over fields and rings in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
Jordan algebras over fields and rings (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for jordan algebras over fields and rings
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks
17C36 Associated manifolds and spaces
Overview
17C36 studies jordan algebra cohomology and deformations in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
Jordan algebra cohomology and deformations (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for jordan algebra cohomology and deformations
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks
17C37 Associated geometries
Overview
17C37 studies jordan superalgebras in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
Jordan superalgebras (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for jordan superalgebras
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks
17C40 Exceptional Jordan structures
Overview
17C40 studies quadratic jordan algebras in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
Quadratic Jordan algebras (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for quadratic jordan algebras
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks
17C50 Jordan algebras: applications to physics
Overview
17C50 studies jordan algebras in geometry and analysis in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
Jordan algebras in geometry and analysis (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for jordan algebras in geometry and analysis
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks
17C55 Finite-dimensional structures
Overview
17C55 studies applications of jordan structures in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
Applications of Jordan structures (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for applications of jordan structures
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks
17C60 Division algebras
Overview
17C60 studies finite-dimensional jordan algebras in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
Finite-dimensional Jordan algebras (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for finite-dimensional jordan algebras
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks
17C65 Jordan structures on Banach spaces and algebras
Overview
17C65 studies infinite-dimensional jordan structures in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
Infinite-dimensional Jordan structures (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for infinite-dimensional jordan structures
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks
17C70 Super structures
Overview
17C70 studies jordan structures and operator algebras in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
Jordan structures and operator algebras (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for jordan structures and operator algebras
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks
17C90 Applications of Jordan algebras
Overview
17C90 studies miscellaneous jordan structures in Jordan structures. It studies commutative but generally nonassociative products governed by Jordan identities and related triple or pair systems.
Related Wikipedia Page
Miscellaneous Jordan structures (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for miscellaneous jordan structures
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in algebraic geometry, functional analysis, and the study of observables in mathematical physics.
Applications
- Jordan identities and structure theory
- Triple systems and pairs
- Applications in geometry and operator theory
References
Recommended Textbooks