Mathematics Branches, Topics, and Sub-Topics

A structured visual guide to the major mathematical areas and their relationships.

Search by code, branch, topic, subtopic, or a keyword from the descriptions.

19Cxx Steinberg groups and related theory ($K_2$)

This subtopic studies Steinberg groups and related K_2 theory, emphasizing relations, symbols, and foundational constructions in algebraic K-theory.

Specific topics

19C09 Central extensions and Schur multipliers

Overview

19C09 studies steinberg groups and universal central extensions in Steinberg groups and related theory K2. It studies the second algebraic K-group and the Steinberg group, linking central extensions, symbols, and commutator relations.

Related Wikipedia Page

Steinberg groups and universal central extensions (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for steinberg groups and universal central extensions
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in group theory, arithmetic, and the structure theory of linear algebraic groups.

Applications

  • Steinberg group and symbols
  • K2 of rings and fields
  • Central extensions and commutator calculus

References

Recommended Textbooks

19C20 Symbols in $K_2$

Overview

19C20 studies matsumoto theorem and related results in Steinberg groups and related theory K2. It studies the second algebraic K-group and the Steinberg group, linking central extensions, symbols, and commutator relations.

Related Wikipedia Page

Matsumoto theorem and related results (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for matsumoto theorem and related results
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in group theory, arithmetic, and the structure theory of linear algebraic groups.

Applications

  • Steinberg group and symbols
  • K2 of rings and fields
  • Central extensions and commutator calculus

References

Recommended Textbooks

19C30 $K_2$ and the Brauer group

Overview

19C30 studies k2 of rings and fields in Steinberg groups and related theory K2. It studies the second algebraic K-group and the Steinberg group, linking central extensions, symbols, and commutator relations.

Related Wikipedia Page

K2 of rings and fields (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for k2 of rings and fields
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in group theory, arithmetic, and the structure theory of linear algebraic groups.

Applications

  • Steinberg group and symbols
  • K2 of rings and fields
  • Central extensions and commutator calculus

References

Recommended Textbooks

19C40 Excision for $K_2$

Overview

19C40 studies applications of k2 in Steinberg groups and related theory K2. It studies the second algebraic K-group and the Steinberg group, linking central extensions, symbols, and commutator relations.

Related Wikipedia Page

Applications of K2 (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for applications of k2
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used in group theory, arithmetic, and the structure theory of linear algebraic groups.

Applications

  • Steinberg group and symbols
  • K2 of rings and fields
  • Central extensions and commutator calculus

References

Recommended Textbooks