Modular Algorithm for Computing Cohomology: Lie Superalgebra of Vector Fields on (2|2)-dimensional Special Odd Symplectic Superspace
نویسنده
چکیده
In this paper we describe an essential improvement of our recent algorithm for computing cohomology of Lie (super)algebra based on partition of the whole cochain complex into minimal subcomplexes. The improvement consists in replacing the arithmetic of rational numbers or integers by much cheaper arithmetic of modular field and using the inequality between the dimensions of cohomology computed over any modular field ZZ/pZZ and over Q: dimZ /pZ H ≥ dimQ H . With this inequality we can, by computing over arbitrary ZZ/pZZ, quickly find those (normally rare) subcomplexes for which dimZ /pZ H > 0 and then carry out the full computation over Q within these subcomplexes. We present also the results of application of corresponding C program to the Lie superalgebra of special vector fields acting on the (2|2)-dimensional odd symplectic supermanifold. In this way we found some new basis elements of cohomology in the trivial module for this algebra.
منابع مشابه
Modular Algorithm for Computing Cohomology: Lie Superalgebra of Special Vector Fields on (2|2)-dimensional Odd-Symplectic Superspace
We describe an essential improvement of our recent algorithm for computing cohomology of Lie (super)algebra based on partition of the whole cochain complex into minimal subcomplexes. We replace the arithmetic of rational numbers or integers by a much cheaper arithmetic of a modular field and use the inequality between the dimensions of cohomology H over any modular field IFp = ZZ/pZZ and over Q...
متن کاملCohomology of aff(1|1) acting on the space of bilinear differential operators on the superspace IR1|1
We consider the aff(1)-module structure on the spaces of bilinear differential operators acting on the spaces of weighted densities. We compute the first differential cohomology of the Lie superalgebra aff(1) with coefficients in space Dλ,ν;µ of bilinear differential operators acting on weighted densities. We study also the super analogue of this problem getting the same results.
متن کاملThe Five Exceptional Simple Lie Superalgebras of Vector Fields
The five simple exceptional complex Lie superalgbras of vector fields are described. One of them is new; the other four are explicitely described for the first time. All of the exceptional Lie superalgebras are obtained with the help of the Cartan prolongation or a generalized prolongation. The description of several of the exceptional Lie superalgebras is associated with the Lie superalgebra a...
متن کاملSuperspace formulation of general massive gauge theories and geometric interpretation of mass–dependent BRST symmetries
A superspace formulation is proposed for the osp(1, 2)–covariant Lagrangian quantization of general massive gauge theories. The superalgebra osp(1, 2) is considered as subalgebra of the superalgebra sl(1, 2) ∼ osp(2, 2) which may be considered as the algebra of generators of the conformal group in a superspace with two anticommuting coordinates. The mass–dependent (anti)BRST symmetries of prope...
متن کاملExplicit Bracket in an Exceptional Simple Lie Superalgebra
This note is devoted to a more detailed description of one of the five simple exceptional Lie superalgebras of vector fields, cvect(0|3)∗, a subalgebra of vect(4|3). We derive differential equations for its elements, and solve these equations. Hence we get an exact form for the elements of cvect(0|3)∗. Moreover we realize cvect(0|3)∗ by ”glued” pairs of generating functions on a (3|3)-dimension...
متن کامل