摘要:

In 1985 K. Saito [Sal] introduced the concept of an extended affine Weyl group (EAWG), the Weyl group of an extended affine root system (EARS). In [A2, Section 5J, we gave a presentation called “a presentation by conjugation” for the class of EAWGs of index zero, a subclass of EAWGs. In this paper we will give a presentation wh.ich we call a “generalized present.ation by conjugation” for the class of reduced EAWGs. If the extended affine Weyl group is of index zero this presentation reduces to “a presentation by conjugation”. Our main result states that when the nullity of the EARS is 2, these two presentations coincide that is, EAWGs of nullity 2 have “a presentation by conjugation”. In [ST] another presentation for EAWGs of nullity 2 is given.

ISSN:0092-7872    

DOI:10.1080/00927870008841084

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008841085

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

RAloops induced by Cayley-Dickson algebras are constructed. AnyRAloop is a homomorphic image of an inducedRAloop. The category of Cayley-Dickson algebras and the category of inducedRAloops are equivalent.

ISSN:0092-7872    

DOI:10.1080/00927870008841086

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

In this paper we establish a relationship between alternative loop algebras and Cayley-Dickson algebras: any Cayley-Dickson algebra is a quotient algebra of an alternative loop algebra. Thus we give a new way of representing a Cayley-Dickson algebra. As an application, a result of Luiz G. X. de Barros is generalized.

ISSN:0092-7872    

DOI:10.1080/00927870008841087

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

ISSN:0092-7872    

DOI:10.1080/00927870008826823

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor