Results 1 to 10 of about 2,124,931 (376)

Categorified central extensions, étale Lie 2-groups and Lie's Third Theorem for locally exponential Lie algebras [PDF]

Adv. Math. 228 (2011) 2218-2257, 2008
Lie's Third Theorem, asserting that each finite-dimensional Lie algebra is the Lie algebra of a Lie group, fails in infinite dimensions. The modern account on this phenomenon is the integration problem for central extensions of infinite-dimensional Lie algebras, which in turn is phrased in terms of an integration procedure for Lie algebra cocycles ...
Agore, Baer, Baez, Baez, Baez, Baez, Baez, Blanco, Blohmann, Bourbaki, Bourgin, Breen, Brylinski, Brylinski, Cartan, Cartan, Christoph Wockel, Crainic, Douady, Eilenberg, Forrester-Barker, Glöckner, Glöckner, Glöckner, Henriques, Hofmann, Hofmann, Iglesias-Zemmour, Iglésias, Jacobson, Kiechle, Kriegl, Lang, Lempert, Loday, MacLane, Maier, Mickelsson, Murray, Nagy, Neeb, Neeb, Nikolaus, Nikolaus, Olver, Pflugfelder, Porst, Pradines, Pressley, Schommer-Pries, Schreiber, Smith, Stolz, Stolz, Tseng, Tuynman, van Est, van Est, van Est, Waldorf, Weinstein, Wockel, Wockel, Wockel   +63 more
arxiv   +4 more sources

Commutative post-Lie algebra structures on Lie algebras [PDF]

arXiv, 2015
We show that any CPA-structure (commutative post-Lie algebra structure) on a perfect Lie algebra is trivial. Furthermore we give a general decomposition of inner CPA-structures, and classify all CPA-structures on parabolic subalgebras of simple Lie algebras.
D. Burde, W. Moens
arxiv   +3 more sources

On Z-gradations of twisted loop Lie algebras of complex simple Lie algebras [PDF]

Commun.Math.Phys. 267 (2006) 587-610, 2005
We define the twisted loop Lie algebra of a finite dimensional Lie algebra $\mathfrak g$ as the Fr\'echet space of all twisted periodic smooth mappings from $\mathbb R$ to $\mathfrak g$. Here the Lie algebra operation is continuous. We call such Lie algebras Fr\'echet Lie algebras. We introduce the notion of an integrable $\mathbb Z$-gradation of a Fr\'
A. Kriegl, A. Pressley, A. V. Razumov, A.L. Onishchik, A.N. Leznov, A.V. Razumov, A.V. Razumov, J. Dieudonné, J.H. Kelley, Kh. S. Nirov, R. Hamilton, V.G. Kac, W. Rudin   +12 more
arxiv   +4 more sources

A note on the restricted universal enveloping algebra of a restricted Lie-Rinehart Algebra [PDF]

arXiv, 2015
Lie-Rinehart algebras, also known as Lie algebroids, give rise to Hopf algebroids by a universal enveloping algebra construction, much as the universal enveloping algebra of an ordinary Lie algebra gives a Hopf algebra, of infinite dimension. In finite characteristic, the universal enveloping algebra of a restricted Lie algebra admits a quotient Hopf ...
Schauenburg, Peter
arxiv   +4 more sources

Post-Lie algebra structures for perfect Lie algebras. [PDF]

Commun Algebra
We study the existence of post-Lie algebra structures on pairs of Lie algebras $(\mathfrak{g},\mathfrak{n})$, where one of the algebras is perfect non-semisimple, and the other one is abelian, nilpotent non-abelian, solvable non-nilpotent, simple, semisimple non-simple, reductive non-semisimple or complete non-perfect.
Burde D, Dekimpe K, Monadjem M.
europepmc   +5 more sources

Lie-Algebra of Single-Valued Pentapartitioned Neutrosophic Set [PDF]

Neutrosophic Sets and Systems, 2022
In this article, we procure the concept of single-valued pentapartitioned neutrosophic Lie (in short SVPN-Lie) algebra under single-valued pentapartitioned neutrosophic set (in short SVPN-set) environment.
Suman Das, Rakhal Das, Bimal Shil, Binod Chandra Tripathy   +3 more
doaj   +1 more source

Quantum scars as embeddings of weakly broken Lie algebra representations [PDF]

Physical review B, 2020
Recently, much effort has focused on understanding weak ergodicity breaking in many-body quantum systems that could lead to wavefunction revivals in their dynamics far from equilibrium.
Kieran Bull, Jean-Yves Desaules, Z. Papić   +2 more
semanticscholar   +1 more source

Computations in finite-dimensional Lie algebras [PDF]

Discrete Mathematics & Theoretical Computer Science, 1997
This paper describes progress made in context with the construction of a general library of Lie algebra algorithms, called ELIAS (Eindhoven Lie Algebra System), within the computer algebra package GAP.
A. M. Cohen, W. A. de Graaf, L. Rónyai
doaj   +2 more sources

A Left-Symmetric Structure on The Semi-Direct Sum Real Frobenius Lie Algebra of Dimension 8

Cauchy: Jurnal Matematika Murni dan Aplikasi, 2022
Let  be the Lie algebra of  the semi-direct sum of the real vector space   and the Lie algebra  of the sets of all  real matrices. In this paper, a Frobenius functional is constructed in order for the Lie algebra  to be the real Frobenius Lie algebra of ...
Edi Kurniadi, Nurul Gusriani, Betty Subartini   +2 more
doaj   +1 more source

3-Derivations and 3-Automorphisms on Lie Algebras

Mathematics, 2022
In this paper, first we establish the explicit relation between 3-derivations and 3- automorphisms of a Lie algebra using the differential and exponential map.
Haobo Xia
doaj   +1 more source