Results 21 to 30 of about 16,231 (186)
UNIVERSAL ENVELOPING ALGEBRAS OF PBW TYPE [PDF]
Glasgow Mathematical Journal, 2011 AbstractWe continue our investigation of the general notion of universal enveloping algebra introduced in [A. Ardizzoni, A Milnor–Moore type theorem for primitively generated braided Bialgebras, J. Algebra 327(1) (2011), 337–365]. Namely, we study a universal enveloping algebra when it is of Poincaré–Birkhoff–Witt (PBW) type, meaning that a suitable ...
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Universal Enveloping Algebras of Lie Antialgebras [PDF]
Algebras and Representation Theory, 2010 Lie antialgebras is a class of supercommutative algebras recently appeared in symplectic geometry. We define the notion of enveloping algebra of a Lie antialgebra and study its properties. We show that every Lie antialgebra is canonically related to a Lie superalgebra and prove that its enveloping algebra is a quotient of the enveloping algebra of the ...
Leidwanger, Séverine +1 more
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New models for some free algebras of small ranks
Karpatsʹkì Matematičnì Publìkacìï, 2023 Dimonoids, generalized digroups and doppelsemigroups are algebras defined on a set with two binary associative operations. The notion of a dimonoid was introduced by J.-L.
A.V. Zhuchok, G.F. Pilz
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First quantization of braided Majorana fermions
Nuclear Physics B, 2022 A Z2-graded qubit represents an even (bosonic) “vacuum state” and an odd, excited, Majorana fermion state. The multiparticle sectors of N, braided, indistinguishable Majorana fermions are constructed via first quantization.
Francesco Toppan
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Gluing affine Yangians with bi-fundamentals
Journal of High Energy Physics, 2020 The affine Yangian of gl 1 $$ {\mathfrak{gl}}_1 $$ is isomorphic to the universal enveloping algebra of W 1 + ∞ $$ {\mathcal{W}}_{1+\infty } $$ and can serve as a building block in the construction of new vertex operator algebras. In [1], a two-parameter
Wei Li
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Twist Deformations of the Supersymmetric Quantum Mechanics [PDF]
, 1997 The N-extended Supersymmetric Quantum Mechanics is deformed via an abelian twist which preserves the super-Hopf algebra structure of its Universal Enveloping Superalgebra. Two constructions are possible.
A Giveon +14 more
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Unified Treatment of a Class of Spherically Symmetric Potentials: Quasi-Exact Solution
Advances in High Energy Physics, 2016 We investigate the Schrödinger equation for a class of spherically symmetric potentials in a simple and unified manner using the Lie algebraic approach within the framework of quasi-exact solvability.
H. Panahi, M. Baradaran
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Group-Graded By-Product Construction and Group Double Centralizer Properties
Mathematics, 2022 For a group π with unit e, we introduce and study the notion of a π-graded Hopf algebra. Then we introduce and construct a new braided monoidal category HHeYDπ over a π-graded Hopf algebra H. We introduce the notion of a π-double centralizer property and
Senlin Zhang, Shuanhong Wang
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A note on the restricted universal enveloping algebra of a restricted Lie-Rinehart Algebra
, 2015 Lie-Rinehart algebras, also known as Lie algebroids, give rise to Hopf algebroids by a universal enveloping algebra construction, much as the universal enveloping algebra of an ordinary Lie algebra gives a Hopf algebra, of infinite dimension.
Schauenburg, Peter
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Do $n$-Lie algebras have universal enveloping algebras
, 2015 The aim of this paper is to investigate in which sense, for $n\geq 3$, $n$-Lie algebras admit universal enveloping algebras. There have been some attempts at a construction (see [10] and [5]) but after analysing those we come to the conclusion that they cannot be valid in general. We give counterexamples and sufficient conditions.
Garcia Martinez, Xabier +2 more
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