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We analyse infinitesimal deformations of morphisms of locally free sheaves on a smooth projective variety $X$ over an algebraically closed field of characteristic zero. In particular, we describe a differential graded Lie algebra…

Algebraic Geometry · Mathematics 2025-03-05 Donatella Iacono , Elena Martinengo

The purpose of this paper is to study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We introduce a suitable cohomology and discuss Infinitesimal deformations, equivalent deformations and…

Rings and Algebras · Mathematics 2017-10-23 Anja Arfa , Nizar Ben Fraj , Abdenacer Makhlouf

In this paper we define Courant algebroids in a purely algebraic way and study their deformation theory by using two different but equivalent graded Poisson algebras of degree -2. First steps towards a quantization of Courant algebroids are…

Quantum Algebra · Mathematics 2011-09-23 Frank Keller , Stefan Waldmann

We study deformations of symplectic structures on a smooth manifold $M$ via the quasi-Poisson theory. By a fact, we can deform a given symplectic structure $\omega $ to a new symplectic structure $\omega_t$ parametrized by some element $t$…

Differential Geometry · Mathematics 2016-05-10 Tomoya Nakamura

We develop the Lie theory of Lie-admissible algebras whose product is enriched with higher operations modeled on directed graphs with a view to apply it to the deformation theories controlled by this kind of Lie algebras. We produce…

Quantum Algebra · Mathematics 2025-10-10 Ricardo Campos , Bruno Vallette

In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative) Poisson algebras and coefficient (noncommutative)…

Quantum Algebra · Mathematics 2022-09-27 Jiefeng Liu , Hongyu Zhou

In this article we construct a cochain complex of a complex Clifford algebra with coefficients in itself in a combinatorial fashion and we call the corresponding cohomology by {\it Clifford cohomology.} We show that {\it Clifford…

Algebraic Topology · Mathematics 2022-12-19 Bikram Banerjee , Goutam Mukherjee

Any deformation of a Weyl or Clifford algebra can be realized through a change of generators in the undeformed algebra. q-Deformations of Weyl or Clifford algebrae that were covariant under the action of a simple Lie algebra g are…

q-alg · Mathematics 2014-11-18 Gaetano Fiore

We define and study coisotropic structures on morphisms of commutative dg algebras in the context of shifted Poisson geometry, i.e. $P_n$-algebras. Roughly speaking, a coisotropic morphism is given by a $P_{n+1}$-algebra acting on a…

Algebraic Geometry · Mathematics 2018-10-03 Valerio Melani , Pavel Safronov

This paper discusses the notion of a deformation quantization for an arbitrary polynomial Poisson algebra A. We examine the Hochschild cohomology group H^3(A) and find that if a deformation of A exists it can be given by bidifferential…

Quantum Algebra · Mathematics 2007-05-23 Michael Penkava , Pol Vanhaecke

We show that the algebras describing blocks of the category of cuspidal weight (respectively generalized weight) $\mathfrak{sl}_n$-modules are one-parameter (respectively multi-parameter) deformations of certain Brauer tree algebras. We…

Representation Theory · Mathematics 2011-09-08 Volodymyr Mazorchuk , Catharina Stroppel

We will demonstrate how calculations in toric geometry can be used to compute quantum corrections to the relations in the chiral ring for certain gauge theories. We focus on the gauge theory of the del Pezzo 2, and derive the chiral ring…

High Energy Physics - Theory · Physics 2010-12-03 Samuel Pinansky

The deformations of an infinite dimensional algebra may be controlled not just by its own cohomology but by that of an associated diagram of algebras, since an infinite dimensional algebra may be absolutely rigid in the classical…

Quantum Algebra · Mathematics 2012-08-28 Murray Gerstenhaber , Anthony Giaquinto

In this paper we investigate the possibility of constructing a complete quantization procedure consisting of geometric and deformation quantization. The latter assigns a noncommutative algebra to a symplectic manifold, by deforming the…

Mathematical Physics · Physics 2008-09-12 Christoph Nölle

These notes present an introduction to an analytic version of deformation quantization. The central point is to study algebras of physical observables and their irreducible representations. In classical mechanics one deals with real Poisson…

High Energy Physics - Theory · Physics 2007-05-23 N. P. Landsman

Consider the functor describing deformations of a representation of the fundamental group of a variety X. This paper is chiefly concerned with establishing an analogue in finite characteristic of a result proved by Goldman and Millson for…

Algebraic Geometry · Mathematics 2019-07-04 J. P. Pridham

In this paper, we study compatible Leibniz algebras. We characterize compatible Leibniz algebras in terms of Maurer-Cartan elements of a suitable differential graded Lie algebra. We define a cohomology theory of compatible Leibniz algebras…

Rings and Algebras · Mathematics 2023-05-03 Abdenacer Makhlouf , Ripan Saha

To study coisotropic reduction in the context of deformation quantization we introduce constraint manifolds and constraint algebras as the basic objects encoding the additional information needed to define a reduction. General properties of…

Quantum Algebra · Mathematics 2023-10-10 Marvin Dippell

We introduce a new cohomology for Lie algebroids, and prove that it provides a differential graded Lie algebra which ``controls'' deformations of the structure bracket of the algebroid. We also have a closer look at various special cases…

Differential Geometry · Mathematics 2007-05-23 M. Crainic , I. Moerdijk

In this paper, we develop a new approach to the deformation theory of restricted Lie-Rinehart algebras in positive characteristic, based on the deformation theory of restricted morphisms introduced in our earlier work. We provide a full…

Representation Theory · Mathematics 2025-07-10 Quentin Ehret