TENSOR PRODUCTS OF STEINBERG ALGEBRAS
| Autor: | Simon W. Rigby |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
16S10
16S99 22A22 ETALE GROUPOID ALGEBRAS ASTERISK-ISOMORPHISM diagonal-preserving isomorphisms General Mathematics Diagonal Steinberg algebras INVERSE SEMIGROUP ample groupoids 01 natural sciences Combinatorics Leavitt algebras Mathematics::K-Theory and Homology 0103 physical sciences FOS: Mathematics 0101 mathematics Mathematics Mathematics::Operator Algebras LEAVITT PATH ALGEBRAS 010102 general mathematics Mathematics - Rings and Algebras Inverse semigroup Mathematics and Statistics Tensor product Rings and Algebras (math.RA) Universal property SIMPLICITY 010307 mathematical physics Isomorphism |
| Zdroj: | JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY |
| ISSN: | 1446-8107 1446-7887 |
| DOI: | 10.1017/s1446788719000302 |
| Popis: | We prove that $A_{R}(G)\otimes _{R}A_{R}(H)\cong A_{R}(G\times H)$ if $G$ and $H$ are Hausdorff ample groupoids. As part of the proof, we give a new universal property of Steinberg algebras. We then consider the isomorphism problem for tensor products of Leavitt algebras, and show that no diagonal-preserving isomorphism exists between $L_{2,R}\otimes L_{3,R}$ and $L_{2,R}\otimes L_{2,R}$ . In fact, there are no unexpected diagonal-preserving isomorphisms between tensor products of finitely many Leavitt algebras. We give an easy proof that every $\ast$ -isomorphism of Steinberg algebras over the integers preserves the diagonal, and it follows that $L_{2,\mathbb{Z}}\otimes L_{3,\mathbb{Z}}\not \cong L_{2,\mathbb{Z}}\otimes L_{2,\mathbb{Z}}$ (as $\ast$ -rings). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|