# Groups, Rings, Lie and Hopf Algebras by Yuri Bahturin, Susan Montgomery, Mikhail Zaicev (auth.),

By Yuri Bahturin, Susan Montgomery, Mikhail Zaicev (auth.), Yuri Bahturin (eds.)

The quantity is nearly fullyyt composed of the examine and expository papers by way of the contributors of the foreign Workshop "Groups, jewelry, Lie and Hopf Algebras", which was once held on the Memorial collage of Newfoundland, St. John's, NF, Canada. All 4 components from the name of the workshop are coated. additionally, a few chapters comment on the subjects, which belong to 2 or extra parts whilst.

*Audience:* The readership particular contains researchers, graduate and senior undergraduate scholars in arithmetic and its functions.

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**Additional resources for Groups, Rings, Lie and Hopf Algebras**

**Example text**

CK] W. Chin and L. Krop, Injective comodulesfor 2x2 quantum matrices, Comm. , 28(2000), 2043-2057. [CP] V. Chari and A. Pressley, A Guide to Quantum Groups, Carob. Univ. Press, 1994. [CR] C. 'Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Interscience, New York, 1962. [FS] J. Feldfoss and H. , 74(1992), 47 - 67. [Hu] J. Humphreys, Projective modules for SL(2, q), J. Algebra, 25(1973), 513-518. [Ja] J. Jans, On the indecomposable representations of algebras, Ann.

D 3. Proofs of Proposition and Corollaries First we prove Proposition. Arguing on the contrary, assume that for some A E 9 the subgroup (TA, A) of HoIF(A) has no exponent n. Then either T1 =I- 1 in AutF(A) or = 1 and there is a q E Q so that (T~q)n =I- 1 in HolF(A) for some k. In the first case, there are ql, q2 in Q such that ql =I- q2 and An ql A -n = q2. Hence, in view of An E gn, we have that ql 1 q2 E gn, contrary to gn n Q = {I}. <1 On HNN-Extensions In The Class Of Groups Of Large Odd Exponent 51 Now suppose that TA: = 1 and (T~q)n -=I- 1 in HoIF(A) for some q E Q and k.

Feldfoss and H. , 74(1992), 47 - 67. [Hu] J. Humphreys, Projective modules for SL(2, q), J. Algebra, 25(1973), 513-518. [Ja] J. Jans, On the indecomposable representations of algebras, Ann. , (2) 66 (1957),418-429. [Je] A. Jeyakumar, Principal indecomposable representations for the group SL(2, q), J. Algebra, 30(1974), 444-458. [LuI] G. Lusztig, Modular Representation and Quantum Groups, in Classical Groups and Related Topics, Beijing, 1987, Contemporary Mathematics 82, pp. 59-77. [Lu2] G. Lusztig, Finite dimensional Hopf algebras arising from quantized universal enveloping algebras, J.