On deformations and contractions of Lie algebras.
Fialowski, Alice, de Montigny, Marc (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Similarity:
Displaying similar documents to “Noncommutative root space Witt, Ricci flow, and Poisson bracket continual Lie algebras.”
On deformations and contractions of Lie algebras.
Quasigraded Lie algebras and modified Toda field equations.
Skrypnyk, Taras V. (2006)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Similarity:
Contractions of Poisson-Lie groups, Lie bialgebras and quantum deformations
Angel Ballesteros, Mariano del Olmo (1997)
Banach Center Publications
Similarity:
Contractions of Poisson-Lie groups are introduced by using Lie bialgebra contractions. As an application, contractions of SL(2,R) Poisson-Lie groups leading to (1+1) Poincaré and Heisenberg structures are analysed. It is shown how the method here introduced allows a systematic construction of the Poisson structures associated to non-coboundary Lie bialgebras. Finally, it is sketched how contractions are also implemented after quantization by using the Lie bialgebra approach. ...
Characteristically nilpotent Lie Algebras: a survey.
José M. Ancochea, Rutwig Campoamor (2001)
Extracta Mathematicae
Similarity:
Fine gradings of low-rank complex Lie algebras and of their real forms.
Svobodová, Milena (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Similarity:
Computations in finite-dimensional Lie algebras.
Cohen, A.M., de Graaf, W.A., Rónyai, L. (1997)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
Similarity:
Poisson-Lie groupoids and the contraction procedure
Kenny De Commer (2015)
Banach Center Publications
Similarity:
On the level of Lie algebras, the contraction procedure is a method to create a new Lie algebra from a given Lie algebra by rescaling generators and letting the scaling parameter tend to zero. One of the most well-known examples is the contraction from 𝔰𝔲(2) to 𝔢(2), the Lie algebra of upper-triangular matrices with zero trace and purely imaginary diagonal. In this paper, we will consider an extension of this contraction by taking also into consideration the natural bialgebra structures...
Drinfeld-Sokolov hierarchies on truncated current Lie algebras
Paolo Casati (2011)
Banach Center Publications
Similarity:
In this paper we construct on truncated current Lie algebras integrable hierarchies of partial differential equations, which generalize the Drinfeld-Sokolov hierarchies defined on Kac-Moody Lie algebras.
Formal differential geometry and Nambu-Takhtajan algebra
Yuri Daletskii, Vitaly Kushnirevitch (1997)
Banach Center Publications
Similarity:
On Lie algebras in braided categories
Bodo Pareigis (1997)
Banach Center Publications
Similarity:
The category of group-graded modules over an abelian group is a monoidal category. For any bicharacter of this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have -ary multiplications between various graded components. They possess universal enveloping algebras that are Hopf algebras in the given category. Their biproducts with the group ring are...
Defining relations for classical Lie superalgebras without Cartan matrices.
Grozman, P., Leites, D., Poletaeva, E. (2002)
Homology, Homotopy and Applications
Similarity:
On classification of metabelian Lie algebras.
Galitski, L.Yu., Timashev, D.A. (1999)
Journal of Lie Theory
Similarity:
Restricted and quasi-toral restricted Lie-Rinehart algebras
Bing Sun, Liangyun Chen (2015)
Open Mathematics
Similarity:
In this paper, we introduce the definition of restrictable Lie-Rinehart algebras, the concept of restrictability is by far more tractable than that of a restricted Lie-Rinehart algebra. Moreover, we obtain some properties of p-mappings and restrictable Lie-Rinehart algebras. Finally, we give some sufficient conditions for the commutativity of quasi-toral restricted Lie-Rinehart algebras and study how a quasi-toral restricted Lie-Rinehart algebra with zero center and of minimal dimension...