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On universal enveloping algebras in a topological setting
, 2014We establish the exponential law for suitably topologies on spaces of vector-valued smooth functions on topological groups, where smoothness is defined by using differentiability along continuous one-parameter subgroups. As an application, we investigate
D. Beltiţă, Mihai Nicolae
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1996
For a complex Lie algebra g, the universal enveloping algebra U(g) is an explicit complex associative algebra with identity having the property that any Lie algebra homomorphism of g into an associative algebra A with identity “extends” to an associative algebra homomorphism of U(g) into A and carrying 1 to 1.
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For a complex Lie algebra g, the universal enveloping algebra U(g) is an explicit complex associative algebra with identity having the property that any Lie algebra homomorphism of g into an associative algebra A with identity “extends” to an associative algebra homomorphism of U(g) into A and carrying 1 to 1.
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Formality and Deformations of Universal Enveloping Algebras
International Journal of Theoretical Physics, 2007The main objective of this paper is to describe the universal enveloping algebras of finite dimensional Lie algebras that satisfy the following constraints: their Hochschild complex, seen as differential graded Lie algebra, is quasi-isomorphic to its Hochschild cohomology. This enlarges and completes previous work of the authors [\textit{M.
Bordemann, Martin, Makhlouf, Abdenacer
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Noetherian enveloping algebras of simple graded Lie algebras
Journal of the Mathematical Society of JapanIt is shown that if the universal enveloping algebra of a simple $\mathbb Z^n$-graded Lie algebra is Noetherian, then the Lie algebra is finite-dimensional.
N. Andruskiewitsch, Olivier Mathieu
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Integral bases for the universal enveloping algebras of map superalgebras
, 2013Let $\mathfrak{g}$ be a finite dimensional complex simple classical Lie superalgebra and $A$ be a commutative, associative algebra with unity over $\mathbb{C}$.
I. Bagci, Samuel Chamberlin
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Some Norms on Universal Enveloping Algebras
Canadian Journal of Mathematics, 1998AbstractThe universal enveloping algebra,U(𝔤), of a Lie algebra 𝔤 supports some norms and seminorms that have arisen naturally in the context of heat kernel analysis on Lie groups. These norms and seminorms are investigated here from an algebraic viewpoint.
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PROJECTIVE MODULES OVER UNIVERSAL ENVELOPING ALGEBRAS
Mathematics of the USSR-Izvestiya, 1985Translation from Izv. Akad. Nauk SSSR, Ser. Mat. 48, No.6, 1123-1137 (Russian) (1984; Zbl 0567.16014)].
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The Universal Enveloping Algebra
2004We have seen that elements of the Lie algebra of a Lie group G are derivations of C ∞ (G). They are thus first-order differential operators that are left-invariant. The universal enveloping algebra is a purely algebraically defined ring that may be identified with the ring of all left-invariant differential operators, including higher-order ones.
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Bimodules and universal enveloping algebras associated to VOAs
Israel Journal of Mathematics, 2021Jianzhi Han
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The Universal Enveloping Algebra
1993As is well known (see §19 of Encycl. Math. Sc. 11) every associative algebra A can be turned into a Lie algebra L(A) by replacing its multiplication (a, b) → ab by the commutator [a, b] = ab — ba. Clearly, every homomorphism of associative algebras is automatically a homomorphism of the corresponding Lie algebras, i.e.
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