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Frobenius algebra at a glance
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Explore the main themes, entities and connections around Frobenius algebra. Start with the topic map, then use the sections below for research and deeper semantic analysis.
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Applications
Properties
Overview
Definition
Key facts & relationships
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Topics to explore
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Overview
- Mathematics
- Representation theory
- Module theory
- Finite-dimensional Dimension (vector space)
- Unital Unital ring
- Associative algebra
- Bilinear form
- Richard Brauer
- Cecil Nesbitt Cecil J. Nesbitt
- Georg Frobenius Ferdinand Georg Frobenius
- Tadashi Nakayama Tadashi Nakayama (mathematician)
- Dieudonné 1958 Frobenius algebra
- Jean Dieudonné
- Quasi-Frobenius rings Quasi-Frobenius ring
- Noetherian rings Noetherian ring
- Regular representation
- Injective Injective module
- Topological quantum field theory
Definition
- Field Field (mathematics)
- Nondegenerate bilinear form
- Linear functional
- Kernel Kernel (algebra)
- Ideal Ideal (ring theory)
- Symmetric Symmetric bilinear form
- Symmetric algebra
- Vector space
Examples
- Matrix algebra Matrix ring
- Trace Trace (linear algebra)
- Endomorphism ring
- Group ring
- Finite group
- Hopf algebra
Properties
- Direct product Product of rings
- Tensor product
- Commutative Commutative ring
- Local Local ring
- Regular module
- Minimal ideal
- Zero-dimensional Krull dimension
- Gorenstein rings Gorenstein ring
- Residue field
- Artinian Artinian ring
- Self-injective Self-injective ring
- Injective Injective object
- Right ideals Right ideal
- Extension field
- Restriction of scalars
- Simple modules Simple module
Category-theoretical definition
Applications
- Representation theory of finite groups
- Number theory
- Algebraic geometry
- Combinatorics
- Coding theory
- Cohomology rings Cohomology ring
- Compact Compact space
- Oriented Orientability
- Manifolds Manifold
- Category Category (category theory)
- Equivalent Equivalence of categories
- Symmetric strong monoidal functors Symmetric monoidal functor
- Cobordisms Cobordism
- Pair of pants Pair of pants (mathematics)
- Khovanov's categorification Khovanov homology
- Jones polynomial
Generalizations
Advanced semantic analysis
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Frobenius algebra
Top relations
Important terminology Word statistics
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Important terminology
frobenius algebra algebras field finite-dimensional ring theory displaystyle right commutative category unital extension associative form also group given called left
Entity relationships Subject–Predicate–Object triples
Extracted RDF-like relationships with confidence and source. The table includes structured facts and lower-confidence contextual relations.| Subject | Predicate | Object | Confidence | Src |
|---|---|---|---|---|
| Frobenius algebra | is a | finite-dimensional unital associative algebra with a special kind of bilinear form which gives the algebras particularly nice duality theories | 0.90 | text |
| Frobenius algebra | is a | k-vector-space A with two multiplication structures as unital Frobenius algebras | 0.90 | text |
| Frobenius algebra | has application | Frobenius | 0.60 | section |
| Frobenius algebra | has application | They | 0.60 | section |
| Frobenius algebra | has application | Hopf | 0.60 | section |
| Frobenius algebra | related to Category-theoretical definition | In | 0.60 | section |
| Frobenius algebra | related to Category-theoretical definition | Frobenius | 0.60 | section |
| Frobenius algebra | related to Definition | Frobenius | 0.60 | section |
| Frobenius algebra | related to Definition | This | 0.60 | section |
| Frobenius algebra | related to Definition | Equivalently | 0.60 | section |
| Frobenius algebra | related to Examples | Any | 0.60 | section |
| Frobenius algebra | related to Examples | Frobenius | 0.60 | section |
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