Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multilinear forms and graded algebras   In this paper we investigate the class of the connected graded algebras which
are finitely generated in degree 1, which are finitely presented with relations
of degrees greater or equal to 2 and which are of finite global dimension D and
Gorenstein. For D greater or equal to 4 we add the condition that these
algebras are homogeneous and Koszul. It is shown that each such algebra is
completely characterized by a multilinear form satisfying a twisted cyclicity
condition and some other nondegeneracy conditions depending on the global
dimension D. This multilinear form plays the role of a volume form and
canonically identifies in the quadratic case to a nontrivial Hochschild cycle
of maximal degree. Several examples including the Yang-Mills algebra and the
extended 4-dimensional Sklyanin algebra are analyzed in this context. Actions
of quantum groups are also investigated.

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The categories of this paper are: eess
7
The categories of this paper are: hep-th
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
3
The categories of this paper are: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: chao-dyn