Soluble groups of matrices over an arbitrary field

10.37236/1729 ◽  
2003 ◽  
Vol 10 (1) ◽  
Author(s):  
Graham Denham

Let $a_1,\ldots,a_n$ be distinct, positive integers with $(a_1,\ldots,a_n)=1$, and let k be an arbitrary field. Let $H(a_1,\ldots,a_n;z)$ denote the Hilbert series of the graded algebra k$[t^{a_1},t^{a_2},\ldots,t^{a_n}]$. We show that, when $n=3$, this rational function has a simple expression in terms of $a_1,a_2,a_3$; in particular, the numerator has at most six terms. By way of contrast, it is known that no such expression exists for any $n\geq4$.


2019 ◽  
Vol 17 (1) ◽  
pp. 1381-1391
Author(s):  
Keli Zheng ◽  
Yongzheng Zhang

Abstract Let 𝔽 be an arbitrary field of characteristic p > 2. In this paper we study irreducible modules with highest weight vectors over Witt and special Lie superalgebras of 𝔽. The same irreducible modules of general and special linear Lie superalgebras, which are the 0-th part of Witt and special Lie superalgebras in certain ℤ-grading, are also considered. Then we establish a certain connection called a P-expansion between these modules.


1995 ◽  
Vol 171 (1) ◽  
pp. 189-203 ◽  
Author(s):  
A. Ballesterbolinches ◽  
K. Doerk ◽  
M.D. Perezramos

2001 ◽  
Vol 31 (1-2) ◽  
pp. 179-192 ◽  
Author(s):  
Michael C. Slattery
Keyword(s):  

2015 ◽  
Vol 105 (2) ◽  
pp. 101-108
Author(s):  
Derek J. S. Robinson
Keyword(s):  

2011 ◽  
Vol 23 (1) ◽  
Author(s):  
Dessislava H. Kochloukova ◽  
Conchita Martínez-Pérez ◽  
Brita E. A. Nucinkis

1994 ◽  
Vol 166 (1) ◽  
pp. 67-70 ◽  
Author(s):  
A. Ballester-Bolinches ◽  
M. D. Pérez-Ramos

Sign in / Sign up

Export Citation Format

Share Document