scholarly journals Eigenvalues of Coxeter Transformations and the Gelfand-Kirillov Dimension of the Preprojective Algebras

1981 ◽  
Vol 83 (2) ◽  
pp. 228 ◽  
Author(s):  
Vlastimil Dlab ◽  
Claus Michael Ringel
2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.


2007 ◽  
Vol 313 (1) ◽  
pp. 165-175 ◽  
Author(s):  
Pavel Etingof ◽  
Frédéric Latour ◽  
Eric Rains

2016 ◽  
Vol 23 (04) ◽  
pp. 701-720 ◽  
Author(s):  
Xiangui Zhao ◽  
Yang Zhang

Differential difference algebras are generalizations of polynomial algebras, quantum planes, and Ore extensions of automorphism type and of derivation type. In this paper, we investigate the Gelfand-Kirillov dimension of a finitely generated module over a differential difference algebra through a computational method: Gröbner-Shirshov basis method. We develop the Gröbner-Shirshov basis theory of differential difference algebras, and of finitely generated modules over differential difference algebras, respectively. Then, via Gröbner-Shirshov bases, we give algorithms for computing the Gelfand-Kirillov dimensions of cyclic modules and finitely generated modules over differential difference algebras.


1998 ◽  
Vol 205 (2) ◽  
pp. 391-412 ◽  
Author(s):  
Karin Erdmann ◽  
Nicole Snashall

2010 ◽  
Vol 323 (5) ◽  
pp. 1369-1407 ◽  
Author(s):  
Roberto Martínez-Villa ◽  
Øyvind Solberg
Keyword(s):  

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