Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Chain extensions of D-algebras and their applications   In order to unify the methods which have been applied to various topics such
as BRST theory of constraints, Poisson brackets of local functionals, and
certain developments in deformation theory, we formulate a new concept which we
call the {\it chain extension} of a $D$-algebra. We develop those aspects of
this new idea which are central to applications to algebra and physics. Chain
extensions may be regarded as generalizations of ordinary algebraic extensions
of Lie algebras. Applications of our theory provide a new constructive approach
to BRST theories which only contains three terms; in particular, this provides
a new point of view concerning consistent deformations. Finally, we show how
Lie algebra deformations are encoded into the structure maps of an sh-Lie
algebra with three terms.

4
The categories of this paper are: cond-mat
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con