Results 21 to 30 of about 2,143,040 (330)

The Hopf Algebra of Fliess Operators and Its Dual Pre-lie Algebra [PDF]

, 2013
We study the Hopf algebra H of Fliess operators coming from Control Theory in the one-dimensional case. We prove that it admits a graded, finite-dimensional, connected grading. Dually, the vector space ℝ ⟨ x 0, x 1 ⟩ is both a pre-Lie algebra for the pre-
L. Foissy
semanticscholar   +1 more source

Lie Bialgebras on the Rank Two Heisenberg–Virasoro Algebra

Mathematics, 2023
The rank two Heisenberg–Virasoro algebra can be viewed as a generalization of the twisted Heisenberg–Virasoro algebra. Lie bialgebras play an important role in searching for solutions of quantum Yang–Baxter equations.
Yihong Su, Xue Chen
doaj   +1 more source

Lie subalgebras of so(3,1) up to conjugacy [PDF]

Arab Journal of Mathematical Sciences, 2022
Purpose – This study aims to find all subalgebras up to conjugacy in the real simple Lie algebra so(3,1). Design/methodology/approach – The authors use Lie Algebra techniques to find all inequivalent subalgebras of so(3,1) in all dimensions.
Ryad Ghanam, Gerard Thompson, Narayana Bandara   +2 more
doaj   +1 more source

Cohomology and deformations of compatible Hom-Lie algebras [PDF]

, 2022
In this paper, we consider compatible Hom-Lie algebras as a twisted version of compatible Lie algebras. Compatible Hom-Lie algebras are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible Hom-Lie algebras generalizing the recent work of Liu, Sheng and Bai.
arxiv   +1 more source

Post-Lie algebra structures and generalized derivations of semisimple Lie algebras [PDF]

, 2011
We study post-Lie algebra structures on pairs of Lie algebras (g,n), and prove existence results for the case that one of the Lie algebras is semisimple.
D. Burde, K. Dekimpe
semanticscholar   +1 more source

Braiding via geometric Lie algebra actions [PDF]

Compositio Mathematica, 2010
We introduce the idea of a geometric categorical Lie algebra action on derived categories of coherent sheaves. The main result is that such an action induces an action of the braid group associated to the Lie algebra.
Sabin Cautis, J. Kamnitzer
semanticscholar   +1 more source

Affine actions on Lie groups and post-Lie algebra structures [PDF]

, 2011
We introduce post-Lie algebra structures on pairs of Lie algebras $(\Lg,\Ln)$ defined on a fixed vector space $V$. Special cases are LR-structures and pre-Lie algebra structures on Lie algebras. We show that post-Lie algebra structures naturally arise in
Burde, Dietrich, Dekimpe, Karel, Vercammen, Kim   +2 more
core   +2 more sources

Abelianizations of derivation Lie algebras of the free associative algebra and the free Lie algebra [PDF]

, 2011
We determine the abelianizations of the following three kinds of graded Lie algebras in certain stable ranges: derivations of the free associative algebra, derivations of the free Lie algebra and symplectic derivations of the free associative algebra. In
S. Morita, Takuya Sakasai, Masaaki Suzuki   +2 more
semanticscholar   +1 more source

Universal enveloping Lie Rota-Baxter algebra of preLie and post-Lie algebras [PDF]

Algebra and Logic, vol. 58, p. 1-14 (2019), 2017
Universal enveloping Lie Rota-Baxter algebras of pre-Lie and post-Lie algebras are constructed. It is proved that the pairs of varieties (Lie Rota-Baxter algebras of zero weight,preLie algebras) and (Lie Rota-Baxter algebras of nonzero weight,post-Lie algebras) are PBW-pairs and the variety of Lie Rota-Baxter algebras is not Schreier.
arxiv   +1 more source

Generalized Reynolds Operators on Lie-Yamaguti Algebras

Axioms, 2023
In this paper, the notion of generalized Reynolds operators on Lie-Yamaguti algebras is introduced, and the cohomology of a generalized Reynolds operator is established.
Wen Teng, Jiulin Jin, Fengshan Long
doaj   +1 more source