Automorphism groups of some algebras |
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| Authors: | Hong Goo Park Jeongsig Lee Seul Hee Choi XueQing Chen Ki-Bong Nam |
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| Institution: | (1) Department of Mathematics, Hanyang University, Seoul, 133-791, Korea;(2) Department of General Studies and Education, SamYuk University, Cheongnyangi, P.O.Box 118, Seoul, 130-650, Korea;(3) Department of Mathematics, University of Jeonju, Chon-ju, 560-759, Korea;(4) Department of Mathematics and Computer Sciences, University of Wisconsin-Whitewater, Whitewater, WI 53190, USA |
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| Abstract: | The automorphism groups of algebras are found in many papers. Using auto-invariance, we find the automorphism groups of the
Laurent extension of the polynomial ring and the quantum n-plane (respectively, twisting polynomial ring) in this work. As an application of the results of this work, we can find the
automorphism group of a twisting algebra. We define a generalized Weyl algebra and show that the generalized Weyl algebra
is simple. We also find the automorphism group of a generalized Weyl algebra. We show that the generalized Weyl algebra A
m,m+n
is the universal enveloping algebra of the generalized Witt algebra W(m,m + n).
This work was supported by 2007 Research fund of Hanyang University |
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| Keywords: | Laurent extension quantum n-plane (generalized) Weyl algebra automorphism auto-invariant |
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