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Related papers: Lie Rinehart Bialgebras for Crossed Products

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In this paper, first we give the notion of a crossed homomorphism on a 3-Lie algebra with respect to an action on another 3-Lie algebra, and characterize it using a homomorphism from a Lie algebra to the semidirect product Lie algebra. We…

Rings and Algebras · Mathematics 2022-12-12 Shuai Hou , Meiyan Hu , Lina Song , Yanqiu Zhou

This article is concerned with crossed products and their applications to random operators. We study the von Neumann algebra of a dynamical system using the underlying Hilbert algebra structure. This gives a particularly easy way to…

Mathematical Physics · Physics 2007-05-23 Daniel H. Lenz

We construct a bialgebra object in the category of linear maps LM from a cocommutative rack bialgebra. The construction does extend to some non-cocommutative rack bialgebras, as is illustrated by a concrete example. As a separate result, we…

Algebraic Topology · Mathematics 2018-10-12 Ulrich Kraehmer , Friedrich Wagemann

We studied both the double cross product and the bicrossproduct constructions for the Hom-Hopf algebras of general $(\alpha,\beta)$-type. This allows us to consider the universal enveloping Hom-Hopf algebras of Hom-Lie algebras, which are…

Rings and Algebras · Mathematics 2019-10-18 S. Halici , A. Karataş , S. Sütlü

A Chern-Weil construction for extensions of Lie-Rinehart algebras is introduced. This generalizes the classical Chern-Weil construction in differential geometry and yields characteristic classes for arbitrary extensions of Lie-Rinehart…

dg-ga · Mathematics 2008-02-03 Johannes Huebschmann

It is shown that a C*-algebra generated by any faithful covariant representation of a Hilbert bimodule X is canonically isomorphic to the crossed product associated to X provided that Rieffel's induced representation functor X-ind is…

Operator Algebras · Mathematics 2015-01-30 B. K. Kwasniewski

In this article we endow the group of bisections of a Lie groupoid with compact base with a natural locally convex Lie group structure. Moreover, we develop thoroughly the connection to the algebra of sections of the associated Lie…

Differential Geometry · Mathematics 2016-01-07 Alexander Schmeding , Christoph Wockel

We consider the extension problem for Lie algebroids over schemes over a field. Given a locally free Lie algebroid Q over a scheme (X,O), and a sheaf of finitely generated Lie O-algebras L, we determine the obstruction to the existence of…

Rings and Algebras · Mathematics 2019-02-12 Ettore Aldrovandi , Ugo Bruzzo , Vladimir Rubtsov

The aim here is to sketch the development of ideas related to brackets and similar concepts: Some purely group theoretical combinatorics due to Ph. Hall led to a proof of the Jacobi identity for the Whitehead product in homotopy theory.…

History and Overview · Mathematics 2022-08-05 Johannes Huebschmann

We introduce the notion of generalized Weyl system, and use it to define *-products which generalize the commutation relations of Lie algebras. In particular we study in a comparative way various *-products which generalize the k-Minkowski…

High Energy Physics - Theory · Physics 2009-11-07 Alessandra Agostini , Fedele Lizzi , Alessandro Zampini

The main aim of this paper is to determine the multiplicative lie algebra structures on the semi-direct product of an abelian group with a group under certain conditions.

Group Theory · Mathematics 2023-05-22 Deepak Pal , Amit Kumar , Sumit Kumar Upadhyay , Seema Kushwaha

The main properties of the crossed product in the category of Hopf algebras are investigated. Let $A$ and $H$ be two Hopf algebras connected by two morphism of coalgebras $\triangleright : H\ot A \to A$, $f:H\ot H\to A$. The crossed product…

Quantum Algebra · Mathematics 2014-02-24 A. L. Agore

Let G and H be two locally compact groups acting on a C*-algebra A by commuting actions. We construct an action on the crossed product AXG out of a unitary 2-cocycle u and the action of H on A. For A commutative, and free and proper actions…

funct-an · Mathematics 2008-02-03 Beatriz Abadie

A Lie superalgebra endowed with a supersymmetric, even, non-degenerate, invariant bilinear form is called a quadratic Lie superalgebra. In this paper we give inductive descriptions of quadratic Lie superalgebras in terms of generalized…

Mathematical Physics · Physics 2007-12-04 I. Bajo , S. Benayadi , M. Bordemann

An involutive Lie bialgebra induces a Batalin-Vilkovisky operator on its exterior algebra. We introduce a graded generalization of the necklace Lie bialgebra, which depends on a choice of a quiver $Q$. We relate the resulting…

Quantum Algebra · Mathematics 2024-06-24 Nikolai Perry , Ján Pulmann

The present paper, though inspired by the use of tensor hierarchies in theoretical physics, establishes their mathematical credentials, especially as genetically related to Lie algebra crossed modules. Gauging procedures in supergravity…

Mathematical Physics · Physics 2023-06-13 Sylvain Lavau , Jim Stasheff

We study formal deformations of hom-Lie-Rinehart algebras. The associated deformation cohomology that controls deformations is constructed using multiderivations of hom-Lie-Rinehart algebras.

Rings and Algebras · Mathematics 2020-07-21 Satyendra Kumar Mishra , Ashis Mandal

In this paper, Lie bialgebra structures on the extended Schrodinger-Virasoro Lie algebra are classified. It is obtained that all the Lie bialgebra structures on L are triangular coboundary. As a by-product, it is derived that the first…

Rings and Algebras · Mathematics 2012-05-01 Lamei Yuan , Yongping Wu , Ying Xu

We classify Lie n-algebras possessing an invariant lorentzian inner product.

Representation Theory · Mathematics 2008-12-18 José Figueroa-O'Farrill

In this paper we study the universal central extension of a Lie--Rinehart algebra and we give a description of it. Then we study the lifting of automorphisms and derivations to central extensions. We also give a definition of a non-abelian…

Rings and Algebras · Mathematics 2014-03-28 José Luis Castiglioni , Xabier García-Martínez , Manuel Ladra