Results 11 to 20 of about 34,345 (209)
PBW Basis of Quantized Universal Enveloping Algebras
Publications of the Research Institute for Mathematical Sciences, 1994 Let \(U_ q= U_ q({\mathfrak g})\) be the quantized universal enveloping algebra of the Lie algebra \({\mathfrak g}\) and \(U_ q^ +\) (resp. \(U_ q^ -\)) be the subalgebra generated by \(e_ i\)'s (resp. \(f_ i\)'s). \textit{G. Lusztig} constructed, by using his PBW base, the canonical base of \(U_ q^ -\) in the case \({\mathfrak g}\) is a finite ...
Yoshihisa Saito
openaire +3 more sources
Algebraic (super-)integrability from commutants of subalgebras in universal enveloping algebras [PDF]
Journal of Physics A: Mathematical and Theoretical, 2022 Starting from a purely algebraic procedure based on the commutant of a subalgebra in the universal enveloping algebra of a given Lie algebra, the notion of algebraic Hamiltonians and the constants of the motion generating a polynomial symmetry algebra is
R. Campoamor-Stursberg +3 more
semanticscholar +1 more source
The structure group for quasi-linear equations via universal enveloping algebras [PDF]
Communications of the American Mathematical Society, 2021 We replace trees by multi-indices as an index set of the abstract model space to tackle quasi-linear singular stochastic partial differential equations.
P. Linares, F. Otto, Markus Tempelmayr
semanticscholar +1 more source
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 In recent years there has been a great interest in the study of Zinbiel (dual Leibniz) algebras. Let A be Zinbiel algebra over an arbitrary field K and let e1,e2,...,em,... be a linear basis of A. In 2010 A.
D.M. Zhangazinova, A.S. Naurazbekova
doaj +1 more source
BERGMAN under MS-DOS and Anick's resolution [PDF]
Discrete Mathematics & Theoretical Computer Science, 1997 Noncommutative algebras, defined by the generators and relations, are considered. The definition and main results connected with the Gröbner basis, Hilbert series and Anicks resolution are formulated.
V. Ufnarovski, S. Cojocaru
doaj +2 more sources
Bulletin of Mathematical Sciences, 2023 Perfect C∗-algebras were introduced by Akeman and Shultz in [Perfect C*-algebras, Mem. Amer. Math. Soc. 55(326) (1985)] and they form a certain subclass of C*-algebras determined by their pure states, and for which the general Stone–Weierstrass ...
Fatmah B. Jamjoom
doaj +1 more source
Carrollian and Galilean conformal higher-spin algebras in any dimensions
Journal of High Energy Physics, 2022 We present higher-spin algebras containing a Poincaré subalgebra and with the same set of generators as the Lie algebras that are relevant to Vasiliev’s equations in any space-time dimension D ≥ 3. Given these properties, they can be considered either as
Andrea Campoleoni, Simon Pekar
doaj +1 more source
Hodge decomposition of string topology
Forum of Mathematics, Sigma, 2021 Let X be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the $S^1$-equivariant homology $ {\overline {\text {H}}}_\ast ^{S^1}({\mathcal {L}} X,{\mathbb {Q}}) $ of the free ...
Yuri Berest +2 more
doaj +1 more source
PBW Property for Associative Universal Enveloping Algebras Over an Operad [PDF]
International mathematics research notices, 2018 Given a symmetric operad $\mathcal{P}$ and a $\mathcal{P}$-algebra $V$, the associative universal enveloping algebra ${\textsf{U}_{\mathcal{P}}}$ is an associative algebra whose category of modules is isomorphic to the abelian category of $V$-modules ...
A. Khoroshkin
semanticscholar +1 more source
On some algebraic formulations within universal enveloping algebras related to superintegrability
Acta Polytechnica, 2022 We report on some recent purely algebraic approaches to superintegrable systems from the perspective of subspaces of commuting polynomials in the enveloping algebras of Lie algebras that generate quadratic (and eventually higher-order) algebras.
Rutwig Campoamor-Stursberg
doaj +1 more source