## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

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Please note: The University of Waterloo is closed for all events until further notice.

Friday, November 8, 2013 — 3:30 PM EST

A collection A of linear operators acting on a finite-dimensional vector space V is said to be transitiveif for any vector y ∈ V and any nonzero vector x ∈ V there exists an element T ∈ A such that Tx = y. When A is itself a linear space, it is clear that this condition is equivalent to the statement that the image of any one-dimensional subspace W of V under A intersects every other one-dimensional subspace non-trivially. A classical theorem of Burnside states that when A is an algebra, this happens precisely if A = L(V), the space of all linear maps on V.

In this talk we shall discuss the following generalization of the notion of transitivity: given an n-dimensional space V as above and integers 1 ≤ k, m ≤ n, we shall say that the algebra A is (k,m)-transitive if for every k-dimensional subspace W of V, the image A(W) = {Tw : T ∈ A,w ∈ W} of W under A intersects every m-dimensional subspace of V non-trivially. An algebra is paratransitive if it is (k,m)-transitive for some k and m. We examine the structure of minimal paratransitive algebras.

This is based upon joint work with L. Livshits, G. MacDonald and H. Radjavi.

Location

MC - Mathematics & Computer Building

5136B

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

200 University Avenue West

Waterloo, ON N2L 3G1

Canada

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1