Abstract
The concept of a Lie supergroup is a generalization of the concept of a Lie group. The idea of this generalization is as follows: Let G 0 be a Lie group, A(G 0) the algebra of infinitely differentiable functions on G 0 w.r.t. the usual addition and multiplication of functions. We denote by φ the map of A(G 0) into the analogous algebra A(G 20 ), where G 20 is the Cartesian product of G 0 by itself: (φf)(g 1, g 2) = f(g 1 g 2). We denote by 0 the automorphism A(G 0): (0f)(g) = f(g −1). Let ε: A(G 0) → K be given by ε(f) = f(e), e being the unit in G 0.
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© 1987 Springer Science+Business Media Dordrecht
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Berezin, F.A. (1987). Lie Supergroups. In: Kirillov, A.A. (eds) Introduction to Superanalysis. Mathematical Physics and Applied Mathematics, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1963-6_8
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DOI: https://doi.org/10.1007/978-94-017-1963-6_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-8392-0
Online ISBN: 978-94-017-1963-6
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