From quantum universal enveloping algebras to quantum algebras
نویسندگان
چکیده
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
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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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We extend the notion of dually conjugate Hopf (super)algebras to the coloured Hopf (super)algebras Hc that we recently introduced. We show that if the standard Hopf (super)algebras Hq that are the building blocks of Hc have Hopf duals H∗ q , then the latter may be used to construct coloured Hopf duals Hc∗, endowed with coloured algebra and antipode maps, but with a standard coalgebraic structur...
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Let L be a Lie algebra with universal enveloping algebra U(L). We prove that if H is another Lie algebra with the property that U(L) ∼= U(H) then certain invariants of L are inherited by H. For example, we prove that if L is nilpotent then H is nilpotent with the same class as L. We also prove that if L is nilpotent of class at most two then L is isomorphic to H.
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2008
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/41/30/304038