✦ LIBER ✦

Going Up for Enveloping Algebras of Lie Algebras

✍ Scribed by Boris Širola

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 102 KB
Volume: 243
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8853

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Generalized Reduced Enveloping Algebras

Generalized Reduced Enveloping Algebras for Restricted Lie Algebras

✍ Christopher P Bendel 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 272 KB

We observe that any finite-dimensional indecomposable module for a restricted Lie algebra over an algebraically closed field is a module for a finite-dimensional quotient of the universal enveloping algebra. These algebras form a two-parameter family which generalizes the notion of a reduced envelop

Primeness Criteria for Universal Envelop

Primeness Criteria for Universal Enveloping Algebras of Lie Color Algebras

✍ Kenneth L Price 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 156 KB

We write det L L / 0 q y y if the matrix formed by brackets between elements of a basis of L L is nonsinguy lar. Unlike Lie super algebras, a Lie color algebra L L may have det L L / 0 and a Ž . universal enveloping algebra U L L which is not prime. We will provide examples Ž . and show that U L L i

Intermediate Growth in Lie Algebras and

Intermediate Growth in Lie Algebras and Their Enveloping Algebras

✍ V.M. Petrogradsky 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 276 KB

In this paper a series of dimensions is suggested which includes as first terms dimension of a vector space, Gelfand᎐Kirillov dimension, and superdimension. In terms of these dimensions we describe the change of a growth in transition from a Lie algebra to its universal enveloping algebra. Also, we

Lie Stacks and Their Enveloping Algebras

✍ Lieven Le Bruyn 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 437 KB

Lie stack is an algebra morphism s : A Ä A B where A and B are finite dimensional C-algebras with B being augmented local. We construct the enveloping algebra U(s) of a Lie stack and show that it is an irreducible Hopf algebra domain with a Poincare Birkhoff Witt basis. We recover the enveloping alg

Gröbner–Shirshov Bases for Lie Superalge

Gröbner–Shirshov Bases for Lie Superalgebras and Their Universal Enveloping Algebras

✍ Leonid A Bokut; Seok-Jin Kang; Kyu-Hwan Lee; Peter Malcolmson 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 231 KB

We show that a set of monic polynomials in a free Lie superalgebra is a Grobner᎐Shirshov basis for a Lie superalgebra if and only if it is a Grobner᎐Shirshov basis for its universal enveloping algebra. We investigate the structure of Grobner᎐Shirshov bases for Kac᎐Moody superalgebras and give ëxplic

Symmetric Pairs for Quantized Enveloping

Symmetric Pairs for Quantized Enveloping Algebras

✍ Gail Letzter 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 290 KB

Let θ be an involution of a semisimple Lie algebra g, let g θ denote the fixed Lie subalgebra, and assume the Cartan subalgebra of g has been chosen in a suitable way. We construct a quantum analog of U g θ which can be characterized as the unique subalgebra of the quantized enveloping algebra of g