Results 51 to 60 of about 1,304,850 (179)

From Loop Groups to 2-Groups [PDF]

, 2005
We describe an interesting relation between Lie 2-algebras, the Kac-Moody central extensions of loop groups, and the group String(n). A Lie 2-algebra is a categorified version of a Lie algebra where the Jacobi identity holds up to a natural isomorphism ...
Baez, John C., Crans, Alissa S., Schreiber, Urs, Stevenson, Danny   +3 more
core   +2 more sources

η and λ deformations as E-models

Nuclear Physics B, 2015
We show that the so-called λ deformed σ-model as well as the η deformed one belong to a class of the E-models introduced in the context of the Poisson–Lie-T-duality. The λ and η theories differ solely by the choice of the Drinfeld double; for the λ model
Ctirad Klimčík
doaj   +1 more source

Local Second Order Sobolev Regularity for p-Laplacian Equation in Semi-Simple Lie Group

Mathematics
In this paper, we establish a structural inequality of the ∞-subLaplacian ▵0,∞ in a class of the semi-simple Lie group endowed with the horizontal vector fields X1,…,X2n.
Chengwei Yu, Yue Zeng
doaj   +1 more source

An Integrability Condition for Simple Lie Groups II [PDF]

Symmetry, Integrability and Geometry: Methods and Applications, 2015
It is shown that a simple Lie group $G$ ($ \neq {\rm SL}_2$) can be locally characterised by an integrability condition on an $\operatorname{Aut}(\mathfrak{g})$ structure on the tangent bundle, where $\operatorname{Aut}(\mathfrak{g})$ is the automorphism group of the Lie algebra of $G$.
openaire   +3 more sources

Fusion Systems and Rank $2$ Simple Groups of Lie Type

Forum of Mathematics, Sigma
For any prime p and S a p-group isomorphic to a Sylow p-subgroup of a rank $2$ simple group of Lie type in characteristic p, we determine all saturated fusion systems supported on S up to isomorphism.
Martin van Beek
doaj   +1 more source

Involutive representations of coordinate algebras and quantum spaces

Journal of High Energy Physics, 2017
We show that s u 2 $$ \mathfrak{s}\mathfrak{u}(2) $$ Lie algebras of coordinate operators related to quantum spaces with s u 2 $$ \mathfrak{s}\mathfrak{u}(2) $$ noncommutativity can be conveniently represented by SO(3)-covariant poly-differential ...
Tajron Jurić, Timothé Poulain, Jean-Christophe Wallet   +2 more
doaj   +1 more source

Restricted simple Lie algebras and their infinitesimal deformations

, 2006
In this expository paper, we first review the classification of the restricted simple Lie algebras in characteristic different from 2 and 3 and then we describe their infinitesimal deformations.
Viviani, Filippo
core   +1 more source

Representations of Complex Semi-simple Lie Groups and Lie Algebras [PDF]

, 2013
31 pages, LaTeX; to appear in a special volume of "Texts and Readings In Mathematics (TRIM)", Hindustan Book Agency.
openaire   +2 more sources

On framed simple Lie groups

Journal of the Mathematical Society of Japan, 2016
For a compact simple Lie group $G$, we show that the element $[G, \mathcal{L}] \in \pi^S_*(S^0)$ represented by the pair $(G, \mathcal{L})$ is zero, where $\mathcal{L}$ denotes the left invariant framing of $G$. The proof relies on the method of E. Ossa [Topology, 21 (1982), 315–323].
openaire   +2 more sources

Poisson-Lie duals of the η deformed symmetric space sigma model

Journal of High Energy Physics, 2017
Poisson-Lie dualising the η deformation of the G/H symmetric space sigma model with respect to the simple Lie group G is conjectured to give an analytic continuation of the associated λ deformed model.
Ben Hoare, Fiona K. Seibold
doaj   +1 more source