arXiv subjects

Teodor Stefan Bildea

Publications and source records attributed to Teodor Stefan Bildea.

3 recordsLinked to original sources

arXiv2006

On the Laplacian subalgebra of certain tensors of group von Neumann algebras

In this paper, we exhibit strongly singular maximal abelian subalgebras living inside certain k-folded tensors of von Neumann group factors. The two classes of groups under consideration are the free groups of rank greater than 2 and the free product of m>2 groups, all finite and having the same order p>2 (m>p-1). We prove actually more, namely that the unique trace preserving conditional expectations from these group factors onto their Laplacian subalgebras are asymptotic homomorphisms, which in turn implies that the subalgebras are strongly singular masas.

math.OA↗

arXiv2005

The Laplacian subalgebra of the k-folded tensor product of the free group factor with itself is a strongly singular masa

In this paper, we present a new class of strongly singular maximal abelian subalgebras living inside the k-folded tensor product of the free group factor (on N>1 generators). A. Sinclair and R. Smith introduced the class of strongly singular maximal abelian von Neumann algebras (MASA) of type II_1 factors. One of their examples was the Laplacian subalgebra of the free group factor, known to be a singularMASA. Using the techniques presented by A. Sinclair and R.Smith, we show that the Laplacian subalgebra of the k-folded tensor product of the free group factor with itself is a strongly singular MASA.

math.OA↗

arXiv2005

Triangle Joins of SP1 Equivalence Relations and their Cost

Free joins of measure preserving equivalence relations, with or without amalgamation were introduced by Gaboriau, who studied their cost and obtained a formula for the cost of free products of groups. We introduce the notion of triangle join of measure preserving equivalence relations and study their cost. As a consequence we show that the cost of Thompson's group G is 1.

math.GR↗