Introduction to Superanalysis

  title={Introduction to Superanalysis},
  author={Felix Alexandrovich Berezin and Alexander A. Kirillov},
1. Grassmann Algebra.- 2. Superanalysis.- 3. Linear Algebra in Z2-Graded Spaces.- 4. Supermanifolds in General.- 5. Lie Superalgebras.- 1. Lie Superalgebras.- 2. Lie Supergroups.- 3. Laplace-Casimir Operators (General Theory).- 4. Radial Parts of the Laplace Operators on the Lie Supergrouups U(p, q) and C(m, n).- 5. Construction of Representations of Lie Supergroups U(p, q) and C(m, n).- Appendix 1. Particle Spin Dynamics as the Grassmann Variant of Classical Mechanics.- Appendix 2… 

Division Algebras, Supersymmetry and Higher Gauge Theory

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We present a general theory of non-perturbative quantization of a class of hermitian symmetric supermanifolds. The quantization scheme is based on the notion of a super Toeplitz operator on a

Chevalley Supergroups

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N-homogeneous superalgebras

We develop the theory of N-homogeneous algebras in a super setting, with particular emphasis on the Koszul property. To any Hecke operator on a vector superspace, we associate certain superalgebras

A new example of supergroups

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Algebraic Aspects of the Berezinian

Many concepts of linear algebra can be generalized to the Z/2-graded setting, leading to linear superalgebra. Often, a formulation in terms of category theory facilitates this passage, and this e.g.

Super Toeplitz operators and non-perturbative deformation quantization of supermanifolds

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Regarding (i), this problem was first studied by Eastwood and LeBrun in [3], where the space of obstructions to extending a thickening of a given order was identified. We present in this thesis