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superdeterminant
Redirected from "superdeterminants".
Contents
Context
Super-Algebra
Linear algebra
linear algebra higher linear algebra
Ingredients
Basic concepts
ring , A-∞ ring
commutative ring , E-∞ ring
module , ∞-module , (∞,n)-module
field , ∞-field
vector space , 2-vector space
rational vector space
real vector space
complex vector space
topological vector space
linear basis ,
orthogonal basis , orthonormal basis
linear map , antilinear map
matrix (square , invertible , diagonal , hermitian , symmetric , …)
general linear group , matrix group
eigenspace , eigenvalue
inner product , Hermitian form
Gram-Schmidt process
Hilbert space
Theorems
(…)
Contents
Idea
The notion of super determinant or Berezinian is the generalization of the notion of determinant of a matrix from algebra to super algebra .
References
Originally due to Felix Berezin . The first publication explaining the Berezin’s determinant is the article of Berezin’s student V. F. Pakhomov, Automorphisms of the tensor product of Abelian and Grassmannian algebras , Mathematical Notes 1974, 16:1, 624–629 mathnet.ru .
Wikipedia, Berezinian
Deligne’s lectures in P. Deligne , P. Etingof , D.S. Freed , L. Jeffrey, D. Kazhdan , J. Morgan, D.R. Morrison and E. Witten , eds. Quantum Fields and Strings , A course for mathematicians, 2 vols. Amer. Math. Soc. Providence 1999. (web version )
I. L. Buchbinder, S. M. Kuzenko, Ideas and methods of supersymmetry and supergravity; or A walk through superspace
Edward Witten , Notes on supermanifolds and integration , arxiv/1209.2199
Last revised on October 1, 2025 at 14:17:00.
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