Introduction to Superanalysis

@inproceedings{Berezin1987IntroductionTS,
  title={Introduction to Superanalysis},
  author={Felix Alexandrovich Berezin and Alexander A. Kirillov},
  year={1987}
}
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

From the four normed division algebras--the real numbers, complex numbers, quaternions and octonions, of dimension k=1, 2, 4 and 8, respectively--a systematic procedure gives a 3-cocycle on the

Matrix Cartan Superdomains, Super Toeplitz-Operators, and Quantization

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

In the framework of algebraic supergeometry, we give a construction of the scheme-theoretic supergeometric analogue of split reductive algebraic group-schemes, namely affine algebraic supergroups

THE INTEGRAL ON QUANTUM SUPERGROUPS OF TYPE

Quantum groups of type Ar\s generalize the general linear supergroups GL(r\s). We compute the integral on these quantum supergroups and whence derive a quantum analogue of (super) HCIZ integral

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

The ground field is fixed to C in this talk. The notion of supergroups arises in the middle of 1960’s in the study of the Hamiltonian formalism of spin systems ([1]), and it is applied for

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

The purpose of this paper is to construct non-perturbative deformation quantizations of the algebras of smooth functions on Poisson supermanifolds. For the examplesU1¦1 andCm¦n, algebras of super

OBSTRUCTION THEORY FOR SUPERMANIFOLDS AND DEFORMATIONS OF SUPERCONFORMAL STRUCTURES

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
...