Results 151 to 160 of about 16,242 (186)

Formality and Deformations of Universal Enveloping Algebras

International Journal of Theoretical Physics, 2007
The 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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Some Norms on Universal Enveloping Algebras

Canadian Journal of Mathematics, 1998
AbstractThe 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, 1985
Translation 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

2004
We 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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The Universal Enveloping Algebra

1993
As 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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The Isomorphism Problem for Universal Enveloping Algebras of Lie Algebras

Algebras and Representation Theory, 2007
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Riley, David, Usefi, Hamid
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Yangians and universal enveloping algebras

Journal of Soviet Mathematics, 1989
The author constructs an associative algebra A by a two-fold limit procedure taking first the projective limit \(A_ m\) of suitably chosen subalgebras \(A_ m(n)\) of the enveloping algebras U(\({\mathfrak gl}(n))\), and then the direct limit with respect to \(m\to \infty\).
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The Universal Enveloping Algebra

1981
The universal enveloping algebra of a Lie algebra is the analogue of the usual group algebra of a group. It has the analogous function of exhibiting the category of Lie algebra modules as a category of modules for an associative algebra. This becomes more than an analogy when the universal enveloping algebra is viewed with its full Hopf algebra ...
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Universal Enveloping Algebras of $A_infty$-Algebras

This paper explores the construction and properties of universal enveloping algebras in the context of $A_infty$-algebras. $A_infty$-algebras, also known as strongly homotopy associative algebras, generalize associative algebras by relaxing the associativity condition up to a coherent system of higher homotopies. These structures play a crucial role in
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Universal Enveloping Algebras of Lie Antialgebras

2009
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, S��verine, Morier-Genoud, Sophie   +1 more
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