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

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 ) → ℂ 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 ℂ -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...

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 ) ...

Loewy coincident algebra and Q F -3 associated graded algebra

Hiroyuki Tachikawa (2009)

Czechoslovak Mathematical Journal

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We prove that an associated graded algebra R G of a finite dimensional algebra R is Q F (= selfinjective) if and only if R is Q F and Loewy coincident. Here R is said to be Loewy coincident if, for every primitive idempotent e , the upper Loewy series and the lower Loewy series of R e and e R coincide. Q F -3 algebras are an important generalization of Q F algebras; note that Auslander algebras form a special class of these algebras. We prove that for a Loewy coincident algebra R , the associated graded...

On the composition structure of the twisted Verma modules for 𝔰𝔩 ( 3 , ℂ )

Libor Křižka, Petr Somberg (2015)

Archivum Mathematicum

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We discuss some aspects of the composition structure of twisted Verma modules for the Lie algebra 𝔰𝔩 ( 3 , ℂ ) , including the explicit structure of singular vectors for both 𝔰𝔩 ( 3 , ℂ ) and one of its Lie subalgebras 𝔰𝔩 ( 2 , ℂ ) , and also of their generators. Our analysis is based on the use of partial Fourier tranform applied to the realization of twisted Verma modules as D -modules on the Schubert cells in the full flag manifold for SL ( 3 , ℂ ) .

𝔤 -quasi-Frobenius Lie algebras

David N. Pham (2016)

Archivum Mathematicum

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A Lie version of Turaev’s G ¯ -Frobenius algebras from 2-dimensional homotopy quantum field theory is proposed. The foundation for this Lie version is a structure we call a 𝔤 -quasi-Frobenius Lie algebra for 𝔤 a finite dimensional Lie algebra. The latter consists of a quasi-Frobenius Lie algebra ( 𝔮 , β ) together with a left 𝔤 -module structure which acts on 𝔮 via derivations and for which β is 𝔤 -invariant. Geometrically, 𝔤 -quasi-Frobenius Lie algebras are the Lie algebra structures associated to...