Classification of Ring and $C^\ast $-Algebra Direct Limits of Finite-Dimensional Semisimple Real Algebras

• Author(s): K. R. Goodearl, David Handelman,
• Publisher: American Mathematical Soc.
• Pages: 147
• ISBN_10: 082182435X
  ISBN_13: 9780821824351
  
• Language: en
• Categories: Mathematics / Algebra / General , Mathematics / Algebra / Linear , Mathematics / Calculus ,

Description:... Motivated by (i) Elliott's classification of direct limits of countable sequences of finite-dimensional semisimple complex algebras and complex AF C*-algebras, (ii) classical results classifying involutions on finite-dimensional semisimple complex algebras, and (iii) the classification by Handelman and Rossmann of automorphisms of period two on the algebras appearing in (i) we study the real algebras described above and completely classify them, up to isomorphism, Morita equivalence, or stable isomorphism. We also show how our classification easily distinguishes various types of algebras within the given classes, and we partially solve the problem of determining exactly which values are attained by the invariants used in classifying these algebras.