Results 11 to 20 of about 1,532 (216)

Quantized semisimple Lie groups [PDF]

Archivum Mathematicum
Notes taken from a series of lectures by R.
Fioresi R., Yuncken R.
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Connections on Semisimple Lie Groups [PDF]

Transactions of the American Mathematical Society, 1972
The plus and minus connections of Cartan and Schouten, which exist on any Lie group, have the following three properties: (1) the connection is left invariant, (2) the curvature of the connection is zero, (3) the set of maximal geodesics through the identity of the Lie group is equal to the set of one-parameter subgroups of the Lie group.
Robert E. Beck
openaire   +3 more sources

Quantization of semisimple real Lie groups [PDF]

Archivum Mathematicum
We provide a novel construction of quantized universal enveloping $*$-algebras of real semisimple Lie algebras, based on Letzter's theory of quantum symmetric pairs. We show that these structures can be `integrated', leading to a quantization of the group C$^*$-algebra of an arbitrary semisimple algebraic real Lie group.
De Commer, Kenny
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RG flow of integrable E-models

Physics Letters B, 2021
We compute the one- and two-loop RG flow of integrable σ-models with Poisson-Lie symmetry. They are characterised by a twist function with 2N simple poles/zeros and a double pole at infinity.
Falk Hassler
doaj   +1 more source

Further results on q-Lie groups, q-Lie algebras and q-homogeneous spaces

Special Matrices, 2021
We introduce most of the concepts for q-Lie algebras in a way independent of the base field K. Again it turns out that we can keep the same Lie algebra with a small modification.
Ernst Thomas
doaj   +1 more source

Implications for colored HOMFLY polynomials from explicit formulas for group-theoretical structure

Nuclear Physics B, 2022
We have recently proposed [1] a powerful method for computing group factors of the perturbative series expansion of the Wilson loop in the Chern-Simons theory with SU(N) gauge group.
E. Lanina, A. Sleptsov, N. Tselousov
doaj   +1 more source

The sheets of a classical lie algebra [PDF]

, 2005
We consider the adjoint action of a connected complex semisimple group G on its Lie algebra g. A sheet of g is a maximal irreducible subset of g consisting of G-orbits of a fixed dimension.
Im Hof, Andreas Emanuel
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Two Generator Subalgebras Of Lie Algebras. [PDF]

, 2007
In [14] Thompson showed that a finite group G is solvable if and only if every twogenerated subgroup is solvable (Corollary 2, p. 388). Recently, Grunevald et al.
Kevin Bowman, Bowman, Kevin, Vicente R. Varea, Varea, Vicente R., Towers, David A., David A. Towers   +5 more
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Quantised coordinate rings of semisimple groups are unique factorisation domains [PDF]

, 2007
We show that the quantum coordinate ring of a semisimple group is a unique factorisation domain in the sense of Chatters and Jordan in the case where the deformation parameter q is a transcendental ...
Lenagan, T.H., Launois, Stephane
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Poisson-Lie T-duality of WZW model via current algebra deformation

Journal of High Energy Physics, 2020
Poisson-Lie T-duality of the Wess-Zumino-Witten (WZW) model having the group manifold of SU(2) as target space is investigated. The whole construction relies on the deformation of the affine current algebra of the model, the semi-direct sum su 2 ℝ ⊕ ⋅ a $
Francesco Bascone, Franco Pezzella, Patrizia Vitale   +2 more
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