Results 181 to 190 of about 14,501 (209)

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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Universal Enveloping Algebra

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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The universal enveloping algebra of sl2 and the Racah algebra

Communications in Algebra, 2019
Let F denote a field with char F=2. The Racah algebra R is the unital associative F-algebra defined by generators and relations in the following way. The generators are A, B, C, D.
Sarah Bockting-Conrad, Hau-Wen Huang
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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 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

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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Quantized Universal Enveloping Algebras

2020
In this chapter we collect background material on quantized universal enveloping algebras. We give in particular a detailed account of the construction of the braid group action and PBW-bases, and discuss the finite dimensional representation theory in the setting that the base field \( \mathbb {K} \) is an arbitrary field and the deformation parameter
Christian Voigt, Robert Yuncken
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The connection between the universal enveloping C*-algebra and the universal enveloping von Neumann algebra of a JW-algebra

Mathematical Proceedings of the Cambridge Philosophical Society, 1992
AbstractThis article aims to study the relationship between the universal enveloping C*-algebra C*(M) and the universal enveloping von Neumann algebra W*(M), when M is a JW-algebra. In our main result (Theorem 2·7) we show that C*(M) can be realized as the C*-subalgebra of W*(M) generated by M.
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Cohomology of the Universal Enveloping Algebras of Certain Bigraded Lie Algebras

Acta Mathematica Sinica, English Series, 2018
The calculation of \(\mathrm{Ext}_{\mathcal A}^{s,t}(\mathbb Z_p,\mathbb Z_p)\), where \(p\) is an odd prime and \(\mathcal{A}\) the mod \(p\) Steenrod algebra, is of great importance for determining the stable homotopy groups of spheres (via the Adams spectral sequence). Following [\textit{J. P. May}, J.
Zhong, Li Nan, Zhao, Hao, Shen, Wen Huai
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Universal Enveloping Algebras of Lie–Rinehart Algebras as a Left Adjoint Functor

Mediterranean Journal of Mathematics, 2022
Paolo Saracco
exaly