Isomorphisms between infinite matrix rings

2 00 6 Isomorphisms between Leavitt Algebras and Their Matrix Rings

Let K be any field, let L n denote the Leavitt algebra of type (1, n − 1) having coefficients in K, and let M d (L n) denote the ring of d × d matrices over L n. In our main result, we show that M d (L n) ∼ = L n if and only if d and n − 1 are coprime. We use this isomorphism to answer a question posed in [14] regarding isomorphisms between various C*-algebras. Furthermore, our result demonstra...

2 2 Fe b 20 08 ISOMORPHISMS BETWEEN LEAVITT ALGEBRAS AND THEIR MATRIX RINGS

Let K be any field, let L n denote the Leavitt algebra of type (1, n − 1) having coefficients in K, and let M d (L n) denote the ring of d × d matrices over L n. In our main result, we show that M d (L n) ∼ = L n if and only if d and n − 1 are coprime. We use this isomorphism to answer a question posed in [14] regarding isomorphisms between various C*-algebras. Furthermore, our result demonstra...

Isomorphisms of p-adic group rings

A long-standing problem, first posed by Graham Higman [15] and later by Brauer [4] is the “isomorphism problem for integral group rings.” Given finite groups G and H, is it true that ZG = ZH implies G 2: H? Many authors have worked on this question, but progress has been difficult [30]. Perhaps the best positive result was that of Whitcomb in 1968 [37], who showed that the implication G = H hol...

Differential Polynomial Rings of Triangular Matrix Rings

Isomorphisms of Infinite Steiner Triple Systems II

A combinatorial method in conjuction with the results presented in [F] is introduced to prove that for any infinite cardinal κ, and every cardinal λ, 0≤λ≤κ, there are 2 mutually non-isomorphic Steiner triple systems of size κ that admit exactly 2 automorphisms. In particular, there are 2 mutually non-isomorphic rigid Steiner triple systems of size κ.