Left-right noncommutative Poisson algebras

• Autorzy: José Casas , Tamar Datuashvili , Manuel Ladra
• Języki publikacji: EN

Abstrakty

EN

The notions of left-right noncommutative Poisson algebra (NPlr-algebra) and left-right algebra with bracket AWBlr are introduced. These algebras are special cases of NLP-algebras and algebras with bracket AWB, respectively, studied earlier. An NPlr-algebra is a noncommutative analogue of the classical Poisson algebra. Properties of these new algebras are studied. In the categories AWBlr and NPlr-algebras the notions of actions, representations, centers, actors and crossed modules are described as special cases of the corresponding wellknown notions in categories of groups with operations. The cohomologies of NPlr-algebras and AWBlr (resp. of NPr-algebras and AWBr) are defined and the relations between them and the Hochschild, Quillen and Leibniz cohomologies are detected. The cases P is a free AWBr, the Hochschild or/and Leibniz cohomological dimension of P is ≤ n are considered separately, exhibiting interesting possibilities of representations of the new cohomologies by the well-known ones and relations between the corresponding cohomological dimensions.

Słowa kluczowe

EN

Poisson algebra; Algebras with bracket; Leibniz algebra; Representation; Left-right noncommutative Poisson algebra cohomology; Hochschild, Quillen, Leibniz cohomologies; Cohomological dimension; Extension; Action; Universal strict general actor; Center

Kategorie tematyczne

• 17B56: Cohomology of Lie (super)algebras
• 17A32: Leibniz algebras
• 18G60: Other (co)homology theories
• 17B63: Poisson algebras

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 1
• Strony: 57-78

Daty

wydano

2014-01-01

online

2013-10-30

Twórcy

autor

José Casas

• University of Vigo

autor

Tamar Datuashvili

• Andrea Razmadze Mathematical Institute at the Ivane Javakhishvili Tbilisi State University

autor

Manuel Ladra

• University of Santiago de Compostela

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0321-x