superdeterminant (changes) in nLab

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Contents

Idea

The notion of super determinant of orBerezinian is the generalization of the notion of determinant of a matrix from algebra to super algebra.

• supergeometry, quasideterminant, supertrace

• Berezin integral

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