NONLINEARITY OF MATRIX GROUPS
نویسندگان
چکیده
منابع مشابه
Nonlinearity of Matrix Groups
The aim of this short note is to answer a question by Guoliang Yu of whether the group EL3(Z〈x, y〉), where Z〈x, y〉 is the free (non-commutative) ring, has any faithful finite dimensional linear representations over a field. Recall that for every (associative unitary) ring R the group ELn(R) is the subgroup of GLn(R) generated by all n × n-elementary matrices xij(r) = Id + reij (r ∈ R, 1 ≤ i 6= ...
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These two topics are closely related. Here we consider some particular groups which arise most naturally as matrix groups or quotients of them, and special properties of matrix groups which are not shared by arbitrary groups. In representation theory, we consider what we learn about a group by considering all its homomorphisms to matrix groups. This article falls roughly into two parts. In the ...
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A 0-1 matrix A is said to avoid a forbidden 0-1 matrix (or pattern) P if no submatrix of A matches P , where a 0 in P matches either 0 or 1 in A. The theory of forbidden matrices subsumes many extremal problems in combinatorics and graph theory such as bounding the length of Davenport-Schinzel sequences and their generalizations, Stanley and Wilf’s permutation avoidance problem, and Turán-type ...
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A group is usually input into a computer by specifying the group either using a presentation or using a generating set of permutations or matrices. Here we will emphasize the latter approach, referring to [Si3, Si4, Ser1] for details of the other situations. Thus, the basic computational setting discussed here is as follows: a group is given, specified as G = 〈X〉 in terms of some generating set...
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ژورنال
عنوان ژورنال: Journal of Topology and Analysis
سال: 2009
ISSN: 1793-5253,1793-7167
DOI: 10.1142/s1793525309000138