Locally Finite Central Simple Algebras

Tamar Bar-On, Shira Gilat, Eliyahu Matzri, Uzi Vishne

Research output: Contribution to journalArticlepeer-review


We develop a comprehensive theory of algebras over a field which are locally both finite dimensional and central simple. We generalize fundamental concepts of the theory of finite dimensional central simple algebras, and introduce supernatural matrix algebras, the supernatural degree and matrix degree, and so on. We define a Brauer monoid, whose unique maximal subgroup is the classical Brauer group, and show that once infinite dimensional division algebras exist over the field, they are abundant.

Original languageEnglish
Pages (from-to)553-607
Number of pages55
JournalAlgebras and Representation Theory
Issue number2
StatePublished - 2021

Bibliographical note

Funding Information:
The authors are partially supported by Israeli Science Foundation grants no. 1623/16 and 630/17.

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature B.V.


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