Linear and multilinear algebra; matrix theory Multilinear algebra Concept
Exterior algebra
Summary
The exterior algebra of a vector space is the associative algebra generated by the space in which the square of every vector is zero.
Where this leads
25 pages build on this one.
- Koszul complex
- Hodge star operator
- Griffiths transversality
- Schubert calculus
- Kaplansky's theorem on PI rings
- Graded manifold
- Canonical bundle
- Grassmannian
- Hopf's theorem on cohomology of compact Lie groups
- Schubert variety
- Berezin integral
- Schouten–Nijenhuis bracket
- Bott's Morse-theoretic proof of periodicity
- Spencer cohomology
- Posner's theorem
- Plücker coordinates
- (p,q)-form
- Polynomial identity ring
- Geometric algebra
- Supermanifold
- Period map
- Cartan's test for involutivity
- Cartan–Kähler theorem
- Amitsur–Levitzki theorem
- Flag variety
Further reading
- Web https://en.wikipedia.org/wiki/Exterior_algebra, Formal definition
About this page
| Tag | 0MDMZ965VE |
|---|---|
| URI | m2://0MDMZ965VE |
| Aliases | grassmann-algebra |
| Kind | concept |
| Writing | W1 stated |
| MSC | 15A75 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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