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primary 17b67

Glasgow Mathematical Journal (1)

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EXTENDED QUANTUM ENVELOPING ALGEBRAS OF (2)
WU ZHIXIANG
Journal:

Glasgow Mathematical Journal / Volume 51 / Issue 3 / September 2009

Published online by Cambridge University Press:

01 September 2009, pp. 441-465

Print publication:

September 2009
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In present paper we define a new kind of quantized enveloping algebra of (2). We denote this algebra by Ur,t, where r, t are two non-negative integers. It is a non-commutative and non-cocommutative Hopf algebra. If r = 0, then the algebra Ur,t is isomorphic to a tensor product of the algebra of infinite cyclic group and the usual quantum enveloping algebra of (2) as Hopf algebras. The representation of this algebra is studied.