Affine Nijenhuis Operators and Hochschild Cohomology of Trusses

IF 0.9 3区物理与天体物理 Q2 MATHEMATICS

Symmetry Integrability and Geometry-Methods and Applications Pub Date : 2023-03-22 DOI:10.3842/SIGMA.2023.056

Tomasz Brzezi'nski, J. Papworth

引用次数: 2

Abstract

The classical Hochschild cohomology theory of rings is extended to abelian heaps with distributing multiplication or trusses. This cohomology is then employed to give necessary and sufficient conditions for a Nijenhuis product on a truss (defined by the extension of the Nijenhuis product on an associative ring introduced by Carinena, Grabowski and Marmo in [Internat. J. Modern Phys. A 15 (2000), 4797-4810, arXiv:math-ph/0610011]) to be associative. The definition of Nijenhuis product and operators on trusses is then linearised to the case of affine spaces with compatible associative multiplications or associative affgebras. It is shown that this construction leads to compatible Lie brackets on an affine space.

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桁架的仿射Nijenhuis算子和Hochschild上同调

将经典的Hochschild环上同调理论推广到具有分布乘法或桁架的阿贝尔堆。然后利用该上同调给出特拉斯上的Nijenhuis积（由Carinena、Grabowski和Marmo在[Interat.J.Modern Phys.a 15（2000），4797-4810，arXiv:math-ph/0610011]中引入的结合环上的Niyenhuis乘积的扩展定义）是结合的必要和充分条件。然后将Nijenhuis乘积和算子在桁架上的定义线性化为具有相容关联乘法或关联仿射的仿射空间的情况。证明了这种构造导致仿射空间上的相容李括号。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Symmetry Integrability and Geometry-Methods and Applications 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

4-8 weeks

期刊介绍： Scope Geometrical methods in mathematical physics Lie theory and differential equations Classical and quantum integrable systems Algebraic methods in dynamical systems and chaos Exactly and quasi-exactly solvable models Lie groups and algebras, representation theory Orthogonal polynomials and special functions Integrable probability and stochastic processes Quantum algebras, quantum groups and their representations Symplectic, Poisson and noncommutative geometry Algebraic geometry and its applications Quantum field theories and string/gauge theories Statistical physics and condensed matter physics Quantum gravity and cosmology.