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Related papers: Higher structures for Lie $H$-pseudoalgebras

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The notion of a \emph{higher-order algebroid}, as introduced by J\'o\'zwikowski and Rotkiewicz in their work \emph{Higher-order analogs of Lie algebroids via vector bundle comorphisms} (SIGMA, 2018), generalizes the concepts of a…

Differential Geometry · Mathematics 2024-10-01 Mikołaj Rotkiewicz

Admissible structure constants related to the dual Lie superalgebras of particular Lie superalgebra $({\cal C}^3 + {\cal A})$ are found by straightforward calculations from the matrix form of super Jacobi and mixed super Jacobi identities…

Mathematical Physics · Physics 2017-07-13 A. Eghbali , A. Rezaei-Aghdam

Generalising a previous work of Jiang and Sheng, a cohomology theory for differential Lie algebras of arbitrary weight is introduced. The underlying $L_\infty[1]$-structure on the cochain complex is also determined via a generalised version…

Rings and Algebras · Mathematics 2024-03-28 Weiguo Lyu , Zihao Qi , Jian Yang , Guodong Zhou

A pseudo $H$-type Lie algebra naturally gives rise to a conformal pseudo-subriemannian fundamental graded Lie algebras. In this paper we investigate the prolongations of the associated fundamental graded Lie algebra and the associated…

Differential Geometry · Mathematics 2024-10-01 Tomoaki Yatsui

This paper studies averaging algebras, say, associative algebras endowed with averaging operators. We develop a cohomology theory for averaging algebras and justify it by interpreting lower degree cohomology groups as formal deformations…

K-Theory and Homology · Mathematics 2020-09-25 Kai Wang , Guodong Zhou

Building upon the work of Pavel in [P. Kolesnikov, Journal of Mathematical Physics, 56, 7 (2015)], we first present the cohomology of averaging operators on the Lie conformal algebras and use it to develop the cohomology of averaging Lie…

Rings and Algebras · Mathematics 2024-12-31 Sania Asif , Zhixiang Wu

This paper is concerned by the concept of algebra up to homotopy for a structure defined by two operations $.$ and [,]. An important example of such a structure is the Gerstenhaber algebra (commutatitve and Lie). The notion of Gerstenhaber…

Quantum Algebra · Mathematics 2012-06-21 Walid Aloulou , Didier Arnal , Ridha Chatbouri

In this paper, first we give the controlling algebra of Lie triple systems. In particular, the cohomology of Lie triple systems can be characterized by the controlling algebra. Then using controlling algebras, we introduce the notions of…

Rings and Algebras · Mathematics 2024-03-25 Haobo Xia , Yunhe Sheng , Rong Tang

One of the algebraic structures that has emerged recently in the study of the operator product expansions of chiral fields in conformal field theory is that of a Lie conformal algebra [K]. A Lie pseudoalgebra is a generalization of the…

Quantum Algebra · Mathematics 2007-05-23 B. Bakalov , A. D'Andrea , V. G. Kac

This Master Thesis is devoted to the study of $n$-plectic manifolds and the Strongly Homotopy Lie algebras, also called $L_{\infty}$-algebras, that can be associated to them. Since multisymplectic geometry and $L_{\infty}$-algebras are…

Differential Geometry · Mathematics 2014-02-11 C. S. Shahbazi

This article explores L_Infinity structures -- also known as 'strongly homotopy Lie algebras' -- on 3-dimensional vector spaces with both Z- and Z_2-gradings. Since the Z-graded L_Infinity algebras are special cases of Z_2-graded algebras…

Quantum Algebra · Mathematics 2007-05-23 Marilyn Daily , Alice Fialowski , Michael Penkava

The aim of this paper is to give a survey of nonassociative Hom-algebra and Hom-superalgebra structures. The main feature of these algebras is that the identities defining the structures are twisted by homomorphisms. We discuss…

Rings and Algebras · Mathematics 2010-01-26 Abdenacer Makhlouf

We define closed model category structures on different categories connected to the world of operad algebras over the category C(k) of (unbounded) complexes of k-modules: on the category of operads, on the category of algebras over a fixed…

q-alg · Mathematics 2008-02-03 Vladimir Hinich

Associated to any manifold equipped with a closed form of degree >1 is an `L-infinity algebra of observables' which acts as a higher/homotopy analog of the Poisson algebra of functions on a symplectic manifold. In order to study Lie group…

Differential Geometry · Mathematics 2016-08-17 Martin Callies , Yael Fregier , Christopher L. Rogers , Marco Zambon

In this paper an algebraic model for unbased rational homotopy theory from the perspective of curved Lie algebras is constructed. As part of this construction a model structure for the category of pseudo-compact curved Lie algebras with…

Algebraic Topology · Mathematics 2018-01-16 James Maunder

A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. We show that the Hochschild type cochain complex of a hom-associative algebra carries a homotopy G-algebra structure. As a consequence, we…

Rings and Algebras · Mathematics 2018-11-09 Apurba Das

Barton Zwiebach constructed the `string products' on the Hilbert space of combined conformal field theory of matter and ghosts. It is well-known that the `tree level' specialization of these products forms a strongly homotopy Lie algebra. A…

High Energy Physics - Theory · Physics 2009-10-30 Martin Markl

We show that there is an equivalence of $\infty$-categories between Lie algebroids and certain kinds of curved Lie algebras. For this we develop a method to study the $\infty$-category of curved Lie algebras using the homotopy theory of…

Algebraic Topology · Mathematics 2021-09-06 Damien Calaque , Ricardo Campos , Joost Nuiten

The space of Lie algebra cohomology is usually described by the dimensions of components of certain degree even for the adjoint module as coefficients when the spaces of cochains and cohomology can be endowed with a Lie superalgebra…

K-Theory and Homology · Mathematics 2007-05-23 Alexei Lebedev , Dimitry Leites , Ilya Shereshevskii

In this paper, we generalize Schur-Weyl duality and Morita Theorem on associative algebras to those on associative $H$-pseudoalgebras. Meanwhile, we get a plenty of associative $H$-pseudoalgebras over a cocommutative Hopf algebra $H$.

Rings and Algebras · Mathematics 2021-12-13 Zhixiang Wu