منابع مشابه
Coloured quantum universal enveloping algebras
We define some new algebraic structures, termed coloured Hopf algebras, by combining the coalgebra structures and antipodes of a standard Hopf algebra set H, corresponding to some parameter set Q, with the transformations of an algebra isomorphism group G, herein called colour group. Such transformations are labelled by some colour parameters, taking values in a colour set C. We show that vario...
متن کاملL ± Operators and Quantum Enveloping Algebras ∗
The relations between L operators and the generators in the quantum enveloping algebras are studied. The L operators for UqAN and UqG2 algebras are explicitly expressed by the generators as examples. ∗This work was supported by the National Natural Science Foundation of China and Grant No.LWTZ-1298 of Chinese Academy of Sciences. 1
متن کاملBraided enveloping algebras associated to quantum parabolic subalgebras
Associated to every subset J of nodes of a Dynkin diagram is a standard parabolic subalgebra pJ of the corresponding Lie algebra g, generated by the positive Borel subalgebra of g together with the negative simple generators fj, j ∈ J . Furthermore one has a decomposition of g as a semi-direct product of pJ and the subalgebra n − J generated by the remaining negative simple generators. In the s...
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A Hom-Lie algebra is a triple (L, [−,−], α), where α is a linear self-map, in which the skew-symmetric bracket satisfies an α-twisted variant of the Jacobi identity, called the Hom-Jacobi identity. When α is the identity map, the Hom-Jacobi identity reduces to the usual Jacobi identity, and L is a Lie algebra. Hom-Lie algebras and related algebras were introduced in [1] to construct deformation...
متن کاملDouble-partition Quantum Cluster Algebras
A family of quantum cluster algebras is introduced and studied. In general, these algebras are new, but sub-classes have been studied previously by other authors. The algebras are indexed by double partitions or double flag varieties. Equivalently, they are indexed by broken lines L. By grouping together neighboring mutations into quantum line mutations we can mutate from the cluster algebra of...
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ژورنال
عنوان ژورنال: Journal of Algebra and Its Applications
سال: 2013
ISSN: 0219-4988,1793-6829
DOI: 10.1142/s021949881350031x