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Gerstenhaber and Batalin-Vilkovisky algebras; algebraic, geometric, and physical aspects

Claude Roger (2009)

Archivum Mathematicum

We shall give a survey of classical examples, together with algebraic methods to deal with those structures: graded algebra, cohomologies, cohomology operations. The corresponding geometric structures will be described(e.g., Lie algebroids), with particular emphasis on supergeometry, odd supersymplectic structures and their classification. Finally, we shall explain how BV-structures appear in Quantum Field Theory, as a version of functional integral quantization.

Gorenstein star modules and Gorenstein tilting modules

Peiyu Zhang (2021)

Czechoslovak Mathematical Journal

We introduce the notion of Gorenstein star modules and obtain some properties and a characterization of them. We mainly give the relationship between n -Gorenstein star modules and n -Gorenstein tilting modules, see L. Yan, W. Li, B. Ouyang (2016), and a new characterization of n -Gorenstein tilting modules.

Graded blocks of group algebras with dihedral defect groups

Dusko Bogdanic (2011)

Colloquium Mathematicae

We investigate gradings on tame blocks of group algebras whose defect groups are dihedral. For this subfamily of tame blocks we classify gradings up to graded Morita equivalence, we transfer gradings via derived equivalences, and we check the existence, positivity and tightness of gradings. We classify gradings by computing the group of outer automorphisms that fix the isomorphism classes of simple modules.

Graded quaternion symbol equivalence of function fields

Przemysław Koprowski (2007)

Czechoslovak Mathematical Journal

We present criteria for a pair of maps to constitute a quaternion-symbol equivalence (or a Hilbert-symbol equivalence if we deal with global function fields) expressed in terms of vanishing of the Clifford invariant. In principle, we prove that a local condition of a quaternion-symbol equivalence can be transcribed from the Brauer group to the Brauer-Wall group.

Graph Cohomology, Colored Posets and Homological Algebra in Functor Categories

Jolanta Słomińska (2012)

Bulletin of the Polish Academy of Sciences. Mathematics

The homology theory of colored posets, defined by B. Everitt and P. Turner, is generalized. Two graph categories are defined and Khovanov type graph cohomology are interpreted as Ext* groups in functor categories associated to these categories. The connection, described by J. H. Przytycki, between the Hochschild homology of an algebra and the graph cohomology, defined for the same algebra and a cyclic graph, is explained from the point of view of homological algebra in functor categories.

Graph Monoids.

F.W. Roush, K.H. Kim, L.G. Makar-Limanov (1982)

Semigroup forum

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