Displaying similar documents to “Lie-Rinehart algebras, Gerstenhaber algebras and Batalin-Vilkovisky algebras”

Some module cohomological properties of Banach algebras

Elham Ilka, Amin Mahmoodi, Abasalt Bodaghi (2020)

Mathematica Bohemica

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We find some relations between module biprojectivity and module biflatness of Banach algebras 𝒜 and and their projective tensor product 𝒜 ^ . For some semigroups S , we study module biprojectivity and module biflatness of semigroup algebras l 1 ( S ) .

Characterizations of incidence modules

Naseer Ullah, Hailou Yao, Qianqian Yuan, Muhammad Azam (2024)

Czechoslovak Mathematical Journal

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Let R be an associative ring and M be a left R -module. We introduce the concept of the incidence module I ( X , M ) of a locally finite partially ordered set X over M . We study the properties of I ( X , M ) and give the necessary and sufficient conditions for the incidence module to be an IN-module, -module, nil injective module and nonsingular module, respectively. Furthermore, we show that the class of -modules is closed under direct product and upper triangular matrix modules.

The abelianization of the Johnson kernel

Alexandru Dimca, Richard Hain, Stefan Papadima (2014)

Journal of the European Mathematical Society

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We prove that the first complex homology of the Johnson subgroup of the Torelli group T g is a non-trivial, unipotent T g -module for all g 4 and give an explicit presentation of it as a S y m . H 1 ( T g , C ) -module when g 6 . We do this by proving that, for a finitely generated group G satisfying an assumption close to formality, the triviality of the restricted characteristic variety implies that the first homology of its Johnson kernel is a nilpotent module over the corresponding Laurent polynomial ring, isomorphic...

On generalized CS-modules

Qingyi Zeng (2015)

Czechoslovak Mathematical Journal

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An 𝒮 -closed submodule of a module M is a submodule N for which M / N is nonsingular. A module M is called a generalized CS-module (or briefly, GCS-module) if any 𝒮 -closed submodule N of M is a direct summand of M . Any homomorphic image of a GCS-module is also a GCS-module. Any direct sum of a singular (uniform) module and a semi-simple module is a GCS-module. All nonsingular right R -modules are projective if and only if all right R -modules are GCS-modules.

On the K -theory and Hattori-Stallings traces of minimal primitive factors of enveloping algebras of semisimple Lie algebras : the singular case

Patrick Polo (1995)

Annales de l'institut Fourier

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Let G be a semisimple complex algebraic group and X its flag variety. Let 𝔤 = Lie ( G ) and let U be its enveloping algebra. Let 𝔥 be a Cartan subalgebra of 𝔤 . For μ 𝔥 * , let J μ be the corresponding minimal primitive ideal, let U μ = U / J μ , and let 𝒯 U μ : K 0 ( U m u ) be the Hattori-Stallings trace. Results of Hodges suggest to study this map as a step towards a classification, up to isomorphism or Morita equivalence, of the -algebras U μ . When μ is regular, Hodges has shown that K 0 ( U μ ) K 0 ( X ) . In this case K 0 ( U μ ) is generated by the classes corresponding...

Derived dimension via τ -tilting theory

Yingying Zhang (2021)

Czechoslovak Mathematical Journal

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Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support τ -tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given τ -tilting module.

The variety of dual mock-Lie algebras

Luisa M. Camacho, Ivan Kaygorodov, Viktor Lopatkin, Mohamed A. Salim (2020)

Communications in Mathematics

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We classify all complex 7 - and 8 -dimensional dual mock-Lie algebras by the algebraic and geometric way. Also, we find all non-trivial complex 9 -dimensional dual mock-Lie algebras.

Universal central extension of direct limits of Hom-Lie algebras

Valiollah Khalili (2019)

Czechoslovak Mathematical Journal

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We prove that the universal central extension of a direct limit of perfect Hom-Lie algebras ( i , α i ) is (isomorphic to) the direct limit of universal central extensions of ( i , α i ) . As an application we provide the universal central extensions of some multiplicative Hom-Lie algebras. More precisely, we consider a family of multiplicative Hom-Lie algebras { ( sl k ( å ) , α k ) } k I and describe the universal central extension of its direct limit.

Relative Gorenstein injective covers with respect to a semidualizing module

Elham Tavasoli, Maryam Salimi (2017)

Czechoslovak Mathematical Journal

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Let R be a commutative Noetherian ring and let C be a semidualizing R -module. We prove a result about the covering properties of the class of relative Gorenstein injective modules with respect to C which is a generalization of Theorem 1 by Enochs and Iacob (2015). Specifically, we prove that if for every G C -injective module G , the character module G + is G C -flat, then the class 𝒢ℐ C ( R ) 𝒜 C ( R ) is closed under direct sums and direct limits. Also, it is proved that under the above hypotheses the class 𝒢ℐ C ( R ) 𝒜 C ( R ) ...