17Dxx Other nonassociative structures
This subtopic studies other nonassociative structures, gathering alternative algebraic systems and methods that do not fit the standard Lie or Jordan frameworks.
Specific topics
17D05 Alternative rings
Overview
17D05 studies alternative, flexible, and malcev algebras in other nonassociative structures. It collects nonassociative systems outside the Jordan and Lie families, including loops, quasigroups, and geometric constructions.
Related Wikipedia Page
Alternative, flexible, and Malcev algebras (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for alternative, flexible, and malcev 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 combinatorics, geometry, and the study of algebraic identities beyond associativity.
Applications
- Loops and quasigroups
- Alternative and Malcev methods
- Computational nonassociative algebra
References
Recommended Textbooks
17D10 Mal'tsev rings and algebras
Overview
17D10 studies bruck loops and related structures in other nonassociative structures. It collects nonassociative systems outside the Jordan and Lie families, including loops, quasigroups, and geometric constructions.
Related Wikipedia Page
Bruck loops and related structures (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for bruck loops and related 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 combinatorics, geometry, and the study of algebraic identities beyond associativity.
Applications
- Loops and quasigroups
- Alternative and Malcev methods
- Computational nonassociative algebra
References
Recommended Textbooks
17D15 Right alternative rings
Overview
17D15 studies quasigroups and loops in other nonassociative structures. It collects nonassociative systems outside the Jordan and Lie families, including loops, quasigroups, and geometric constructions.
Related Wikipedia Page
Quasigroups and loops (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for quasigroups and loops
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, geometry, and the study of algebraic identities beyond associativity.
Applications
- Loops and quasigroups
- Alternative and Malcev methods
- Computational nonassociative algebra
References
Recommended Textbooks
17D20 $(\gamma, \delta)$-rings, including $(1, -1)$-rings
Overview
17D20 studies nonassociative algebras associated with geometry in other nonassociative structures. It collects nonassociative systems outside the Jordan and Lie families, including loops, quasigroups, and geometric constructions.
Related Wikipedia Page
Nonassociative algebras associated with geometry (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for nonassociative algebras associated with geometry
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, geometry, and the study of algebraic identities beyond associativity.
Applications
- Loops and quasigroups
- Alternative and Malcev methods
- Computational nonassociative algebra
References
Recommended Textbooks
17D25 Lie-admissible algebras
Overview
17D25 studies cohomology and deformation of nonassociative systems in other nonassociative structures. It collects nonassociative systems outside the Jordan and Lie families, including loops, quasigroups, and geometric constructions.
Related Wikipedia Page
Cohomology and deformation of nonassociative systems (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for cohomology and deformation of nonassociative 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 combinatorics, geometry, and the study of algebraic identities beyond associativity.
Applications
- Loops and quasigroups
- Alternative and Malcev methods
- Computational nonassociative algebra
References
Recommended Textbooks
17D92 Genetic algebras
Overview
17D92 studies computational methods in nonassociative algebra in other nonassociative structures. It collects nonassociative systems outside the Jordan and Lie families, including loops, quasigroups, and geometric constructions.
Related Wikipedia Page
Computational methods in nonassociative algebra (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for computational methods in nonassociative algebra
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, geometry, and the study of algebraic identities beyond associativity.
Applications
- Loops and quasigroups
- Alternative and Malcev methods
- Computational nonassociative algebra
References
Recommended Textbooks
17D93 Baric algebras, train algebras
Overview
17D93 studies applications of nonassociative structures in other nonassociative structures. It collects nonassociative systems outside the Jordan and Lie families, including loops, quasigroups, and geometric constructions.
Related Wikipedia Page
Applications of nonassociative structures (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for applications of nonassociative 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 combinatorics, geometry, and the study of algebraic identities beyond associativity.
Applications
- Loops and quasigroups
- Alternative and Malcev methods
- Computational nonassociative algebra
References
Recommended Textbooks
17D99 None of the above
Overview
17D99 studies none of the above in other nonassociative structures. It collects nonassociative systems outside the Jordan and Lie families, including loops, quasigroups, and geometric constructions.
Related Wikipedia Page
None of the above (Wikipedia)
Useful Links
Key Ideas
- Canonical formulations and representative examples for none of the above
- How structural, local, and computational viewpoints interact in the subject
- Standard theorem patterns and invariants used in current research practice
Typical Uses
Used in combinatorics, geometry, and the study of algebraic identities beyond associativity.
Applications
- Loops and quasigroups
- Alternative and Malcev methods
- Computational nonassociative algebra
References
Recommended Textbooks