Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cohomology of Heisenberg Lie Superalgebras   Suppose the ground field to be algebraically closed and of characteristic
different from $2$ and $3$. All Heisenberg Lie superalgebras consist of two
super versions of the Heisenberg Lie algebras, $\frak{h}_{2m,n}$ and
$\frak{ba}_n$ with $m$ a nonnegative integer and $n$ a positive integer. The
space of a "classical" Heisenberg Lie superalgebra $\frak{h}_{2m,n}$ is the
direct sum of a superspace with a non-degenerate anti-supersymmetric even
bilinear form and a one-dimensional space of values of this form constituting
the even center. The other super analog of the Heisenberg Lie algebra,
$\frak{ba}_n$, is constructed by means of a non-degenerate anti-supersymmetric
odd bilinear form with values in the one-dimensional odd center. In this paper,
we study the cohomology of $\frak{h}_{2m,n}$ and $\frak{ba}_n$ with
coefficients in the trivial module by using the Hochschild-Serre spectral
sequences relative to a suitable ideal. In characteristic zero case, for any
Heisenberg Lie superalgebra, we determine completely the Betti numbers and
associative superalgebra structure for their cohomology. In characteristic
$p>3$ case, we determine the associative superalgebra structures for the
divided power cohomology of $\frak{ba}_n$ and we also make an attempt to
determine the cohomology of $\frak{h}_{2m,n}$ by computing it in a
low-dimensional case.

14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
26
The categories of this paper are: bayes-an