
TL;DR
This paper characterizes simple two-sided vector spaces over perfect fields, computes their Quillen K-theory, and explores related homomorphism structures, advancing understanding of their algebraic and categorical properties.
Contribution
It provides a complete classification of simple two-sided vector spaces over perfect fields and calculates their Quillen K-theory, linking algebraic structures with K-theoretic invariants.
Findings
Complete classification of simple two-sided vector spaces
Calculation of Quillen K-theory for these categories
Description of homomorphisms from fields to matrix rings
Abstract
We study the structure of two-sided vector spaces over a perfect field . In particular, we give a complete characterization of isomorphism classes of simple two-sided vector spaces which are left finite-dimensional. Using this description, we compute the Quillen -theory of the category of left finite-dimensional, two-sided vector spaces over . We also consider the closely related problem of describing homomorphisms .
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
