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Relevant bibliographies by topics / Maurer-Cartan element

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Academic literature on the topic 'Maurer-Cartan element'

Author: Grafiati

Published: 26 April 2025

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Journal articles on the topic "Maurer-Cartan element"

1

Ward, Benjamin. "Maurer–Cartan elements and cyclic operads." Journal of Noncommutative Geometry 10, no. 4 (2016): 1403–64. http://dx.doi.org/10.4171/jncg/263.

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2

Chen, Zhuo, Mathieu Stiénon, and Ping Xu. "Geometry of Maurer-Cartan Elements on Complex Manifolds." Communications in Mathematical Physics 297, no. 1 (2010): 169–87. http://dx.doi.org/10.1007/s00220-010-1029-4.

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3

Das, Apurba, and Satyendra Kumar Mishra. "The L∞-deformations of associative Rota–Baxter algebras and homotopy Rota–Baxter operators." Journal of Mathematical Physics 63, no. 5 (2022): 051703. http://dx.doi.org/10.1063/5.0076566.

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A relative Rota–Baxter algebra is a triple ( A, M, T) consisting of an algebra A, an A-bimodule M, and a relative Rota–Baxter operator T. Using Voronov’s derived bracket and a recent work of Lazarev, Sheng, and Tang, we construct an L∞[1]-algebra whose Maurer–Cartan elements are precisely relative Rota–Baxter algebras. By a standard twisting, we define a new L∞[1]-algebra that controls Maurer–Cartan deformations of a relative Rota–Baxter algebra ( A, M, T). We introduce the cohomology of a relative Rota–Baxter algebra ( A, M, T) and study infinitesimal deformations in terms of this cohomology

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4

Buijs, Urtzi, Yves Félix, Aniceto Murillo, and Daniel Tanré. "Maurer–Cartan Elements in the Lie Models of Finite Simplicial Complexes." Canadian Mathematical Bulletin 60, no. 3 (2017): 470–77. http://dx.doi.org/10.4153/cmb-2017-003-7.

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AbstractIn a previous work, we associated a complete diòerential graded Lie algebra to any finite simplicial complex in a functorial way. Similarly, we also have a realization functor fromthe category of complete diòerential graded Lie algebras to the category of simplicial sets. We have already interpreted the homology of a Lie algebra in terms of homotopy groups of its realization. In this paper, we begin a dictionary between models and simplicial complexes by establishing a correspondence between the Deligne groupoid of the model and the connected components of the finite simplicial complex

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5

Chtioui, T., A. Hajjaji, S. Mabrouk, and A. Makhlouf. "Cohomology and deformations of twisted O-operators on 3-Lie algebras." Filomat 37, no. 21 (2023): 6977–94. http://dx.doi.org/10.2298/fil2321977c.

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The purpose of this paper is to introduce and study twisted O-operators on 3-Lie algebras. We construct an L?-algebra whose Maurer-Cartan elements are twisted O-operators and define a cohomology of a twisted O-operator T as the Chevalley-Eilenberg cohomology of a certain 3-Lie algebra induced by T with coefficients in a suitable representation. Then we consider infinitesimal and formal deformations of twisted O-operators.

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6

Liu, Jiefeng, and Yunhe Sheng. "Homotopy Poisson algebras, Maurer–Cartan elements and Dirac structures of CLWX 2-algebroids." Journal of Noncommutative Geometry 15, no. 1 (2021): 147–93. http://dx.doi.org/10.4171/jncg/398.

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7

Das, Apurba. "Cohomology and deformations of weighted Rota–Baxter operators." Journal of Mathematical Physics 63, no. 9 (2022): 091703. http://dx.doi.org/10.1063/5.0093066.

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Weighted Rota–Baxter operators on associative algebras are closely related to modified Yang–Baxter equations, splitting of algebras, and weighted infinitesimal bialgebras and play an important role in mathematical physics. For any λ ∈ k, we construct a differential graded Lie algebra whose Maurer–Cartan elements are given by λ-weighted relative Rota–Baxter operators. Using such characterization, we define the cohomology of a λ-weighted relative Rota-Baxter operator T and interpret this as the Hochschild cohomology of a suitable algebra with coefficients in an appropriate bimodule. We study lin

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8

Xu, Senrong, Wei Wang, and Jia Zhao. "Twisted Rota-Baxter operators on Hom-Lie algebras." AIMS Mathematics 9, no. 2 (2023): 2619–40. http://dx.doi.org/10.3934/math.2024129.

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<abstract><p>Uchino initiated the investigation of twisted Rota-Baxter operators on associative algebras. Relevant studies have been extensive in recent times. In this paper, we introduce the notion of a twisted Rota-Baxter operator on a Hom-Lie algebra. By utilizing higher derived brackets, we establish an explicit $ L_{\infty} $-algebra whose Maurer-Cartan elements are precisely twisted Rota-Baxter operators on Hom-Lie algebra s. Additionally, we employ Getzler's technique of twisting $ L_\infty $-algebras to establish the cohomology of twisted Rota-Baxter operators. We demonstra

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9

Goncharov, Alexander B. "Hodge correlators." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 748 (2019): 1–138. http://dx.doi.org/10.1515/crelle-2016-0013.

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Abstract Hodge correlators are complex numbers given by certain integrals assigned to a smooth complex curve. We show that they are correlators of a Feynman integral, and describe the real mixed Hodge structure on the pronilpotent completion of the fundamental group of the curve. We introduce motivic correlators, which are elements of the motivic Lie algebra and whose periods are the Hodge correlators. They describe the motivic fundamental group of the curve. We describe variations of real mixed Hodge structures on a variety by certain connections on the product of the variety by twistor plane

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10

HAAK, G., M. SCHMIDT, and R. SCHRADER. "GROUP THEORETIC FORMULATION OF THE SEGAL-WILSON APPROACH TO INTEGRABLE SYSTEMS WITH APPLICATIONS." Reviews in Mathematical Physics 04, no. 03 (1992): 451–99. http://dx.doi.org/10.1142/s0129055x92000121.

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A general group theoretic formulation of integrable systems is presented. The approach generalizes the discussion of the KdV equations of Segal and Wilson based on ideas of Sato. The starting point is the construction of commuting flows on the group via left multiplication with elements from an abelian subgroup. The initial data are then coded by elements, called abstract scattering data, in a certain coset space. The resulting equations of motion are then derived from a suitably formulated Maurer-Cartan equation (zero curvature condition) given an abstract Birkhoff factorization. The resultin

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