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Locally matrix and locally standard algebras and Steinitz numbers
- Speaker(s)
- Bogdana Oliynyk
- Affiliation
- Politechnika Śląska
- Language of the talk
- English
- Date
- Feb. 20, 2025, 12:15 p.m.
- Link
- https://uw-edu-pl.zoom.us/j/98300776179?pwd=rQz64ILq7lBS5bD1bsfHTPtqikClEG.1
- Information about the event
- referat online
- Seminar
- Seminar Algebra
In this talk, based on joint papers with Oksana Bezushchak, we consider parametrization of locally matrix and locally standard algebras by Steinitz numbers. Glimm showed that every countable-dimensional unital locally matrix algebra is uniquely determined by its Steinitz number. We assign a Steinitz number st(A) with uncountable-dimensional unital locally matrix algebra A. We use this assignment to give a negative answer to Kurochkin's question about primary decompositions of locally matrix algebras. We will also discuss a parameterization of countable locally standard algebras by pairs of a Steinitz number and a real number greater or equal to 1. The last parametrization is an analog of the theorems of Dixmier and Baranov.
