Search results for "Free abelian group"
showing 3 items of 3 documents
Abelian gradings on upper-triangular matrices
2003
Let G be an arbitrary finite abelian group. We describe all possible G-gradings on an upper-triangular matrix algebra over an algebraically closed field of characteristic zero.
A note on easy and efficient computation of full abelian periods of a word
2016
Constantinescu and Ilie (Bulletin of the EATCS 89, 167-170, 2006) introduced the idea of an Abelian period with head and tail of a finite word. An Abelian period is called full if both the head and the tail are empty. We present a simple and easy-to-implement $O(n\log\log n)$-time algorithm for computing all the full Abelian periods of a word of length $n$ over a constant-size alphabet. Experiments show that our algorithm significantly outperforms the $O(n)$ algorithm proposed by Kociumaka et al. (Proc. of STACS, 245-256, 2013) for the same problem.
On the classification of CAT(0) structures for the 4-string braid group
2005
This paper is concerned with the class of so-called CAT(0) groups, namely, those groups that admit a geometric (i.e., properly discontinuous, co-compact, and isometric) action on some CAT(0) space. More precisely, we are interested in knowing to what extent it is feasible to classify the geometric CAT(0) actions of a given group (up to, say, equivariant homothety of the space). A notable example of such a classification is the flat torus theorem, which implies that the minimal geometric CAT(0) actions of the free abelian group Z (n ≥ 1) are precisely the free actions by translations of Euclidean space E. Typically, however, a given group will have uncountably many nonequivalent actions, mak…