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arXiv · 2601.03503

Direct limits of graded matrix algebras

Mikhail Kochetov·Felipe Yasumura
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Abstract

The direct limit of finite-dimensional semisimple associative algebras arises as a purely algebraic counterpart to important $C^\ast$-algebras. In this paper, we classify direct limits of matrix algebras endowed with a grading by a finite abelian group over an algebraically closed field. In particular, we give an explicit description of the graded $K_0$ group of the direct limit of matrix algebras, and we provide conditions under which this limit absorbs graded-division algebras.

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Mikhail Kochetov, Felipe Yasumura. 2026-01-07. Direct limits of graded matrix algebras. https://arxiv.org/abs/2601.03503

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