Characteristic Modules of Dual Extensions and Gröbner Bases

Authors: Xu, Yun¹; Li, Long²

Source: Acta Mathematica Sinica, Volume 20, Number 6, November 2004 , pp. 1119-1130(12)

Publisher: Springer

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Abstract:

Let C be a finite dimensional directed algebra over an algebraically closed field k and A = A(C) the dual extension of C. The characteristic modules of A are constructed explicitly for a class of directed algebras, which generalizes the results of Xi. Furthermore, it is shown that the characteristic modules of dual extensions of a certain class of directed algebras admit the left Gröbner basis theory in the sense of E. L. Green.

Keywords: Quasi–hereditary algebra; Dual extension; Characteristic module; (Left) Gröbner basis; 16G20; 13P10

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10114-004-0421-4

Affiliations: 1: Faculty of Mathematics and Computer Science, Hubei University, Wuhan 430062, P. R. China, Email: xuy@hubu.edu.cn 2: Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, P. R. China, Email: lcli@amss.ac.cn

Publication date: 2004-11-01