By K. P. Shum, E. Zelmanov, Jiping Zhang, Li Shangzhi

This quantity is a compilation of lectures on algebras and combinatorics offered on the moment overseas Congress in Algebra and Combinatorics. It stories on not just new effects, but additionally on open difficulties within the box. The court cases quantity turns out to be useful for graduate scholars and researchers in algebras and combinatorics. The participants contain eminent figures akin to E Bannai, P Hilton, M Jambu, I Kotsireas, B Schein and A Smoktunowicz.

**Read or Download Advances In Algebra And Combinatorics: Proceedings of the Second International Congress in Algebra and Cominatorics Guangzhou, China 2 - 4 July 2007; Beijing, China 6 - 11 July 2007; Xian, PDF**

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**Additional info for Advances In Algebra And Combinatorics: Proceedings of the Second International Congress in Algebra and Cominatorics Guangzhou, China 2 - 4 July 2007; Beijing, China 6 - 11 July 2007; Xian,**

**Example text**

77(1955), 279-285. 16. Kokorin A. , Kopytov V. , Linearly ordered groups. Moscow: Nauka, 1972. 17. , Algebra of functions on quantum groups, Part I, Providence R1:Amer. Math. , 1998. 18. , Crossed products and multiplicative analogues of Weyl algebras, J. London Math. 38(1988), N 1, 47-55. 34 19. , Hopf algebras and their actions on rings. Regional Conference Series in Mathematics, v. 82 - American Math. :Providence R. , 1993. 20. Oh Sei-Qwon, Park Chun-Gil, Shin Youg-Yeon, Quantum n-space and Poisson n-space, Commun.

A dual notion of H-comodule algebra is a notion of H-module algebra. We say that an algebra A is an H-module algebra if A is an H-module and h(ab) = C,(h(l)a)(hp)b),where A(h) = Chh(1) @ h ( q . If is a finite dimensional Hopf algebra then H* = Homk(H, k ) is again a Hopf algebra and H** 21 H . An algebra A is an H-module algebra if and only if A is an H*-comodule algebra. In noncommutative geometry 1141 a quantum polynomial algebra 0, with r = 0 is a coordinate algebra of a quantum aEne space A: is considered together with quantum Grassman algebra I?

This application gives an anti-commutative Grobner-Shirshov basis of a free Lie algebra. Let X = {zili E I} be a linear ordered set. Let X** be the set of all non-associative words (u)in X. We assume that (u) is a bracketing of u. Then we define normal words N = { [u]} and order them by using induction on the length n = 1[u]of 1 [u]: (i) If n = 1, then [u] = xi is a normal word. Define zi> xj if i > j. Let Nn-l = {[u]I[u] is a normal word and 1[u]15 n - l}, n > 1 and suppose that ‘‘ < ” is a well order on Nn-l.