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 foreign Congress in Algebra and Combinatorics. It experiences on not just new effects, but in addition on open difficulties within the box. The lawsuits quantity turns out to be useful for graduate scholars and researchers in algebras and combinatorics. The individuals contain eminent figures similar 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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**Extra 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,**

**Sample text**

Now, we order the set N . It is obvious that > is a monomial order on N . Such an order is also called the deg-lex order on N = X * Y * . Let f and g be monic polynomials of k N and w = w x w y E N . Then we have found 16 types of compositions of inclusion and intersection. S is called a Grobner-Shirshov basis in kN = k ( X ) 8 k ( Y ) if all compositions of elements in S are trivial modulo S. 5. Let S k ( X )8 k ( Y ) with each s E S monic and “ < ” the deg-lea: order o n N = X * Y * as before.

Bokut, V. V. Chaynikov and K. P. Shum [8], the authors present the classical results of Artin-Markov on braid groups by using the Grobner-Shirshov bases. As an application, one can reobtain the normal form of Artin-Makov-Ivanovskiy as an easy corollary. 5. 1. Grobner and Grobner-Shirshov bases: an elementary approach There is an elementary approach in L. A. P. Shum [15] to Grobner-Shirshov bases theory with quite a few examples, including the example for Lie algebras. 2. Shirshov’s CD-lemma f o r Lie algebras What is now called the Grobner-Shirshov method for Lie algebras originally invented by A.

Artamonov V. // J. Math. Sci. - 2006. - 134, N 1. - p. 1773 - 1798. 7. , Actions of pointed Hopf algebras on quantum torus, in Proceedings of the ”Ferrara Algebra Workshop” jointly with the ”Workshop on Hopf Algebras, Swansea”, a special issue of the ”Annali dell’universita’ di Ferrara, sez. VII, Scienze Matematiche, Vol. LI, 29-60, 2005. 8. Artamonov V. , Cohn P. , The skew field of rational functions on the quantum plane. 3. Math. Sci. 93(1999), N 6, 824-829. 9. , DBrivations et automorphismes de quelques algkbres quantiques, Comm.