ON LINEAR SPANS OF THE COMMUTATOR SUBGROUPS OF UNITARY GROUPS OF NON-COMMUTATIVE FINITE DIMENSIONAL DIVISION ALGEBRAS
Abstract
Let K/к be a separable quadratic extension, char K ≠ 2, A a non-commutative finite dimensional central K-division algebra with unitary к-involution. For algebras A of prime index relatively prime to char K we prove the following conjecture: к-linear span of the commutator subgroup of а unitary group of A coincides with A.
About the Authors
A. V. Prokopchuk
Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk
Belarus
Belarus
V. I. Yanchevskii
Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk
Belarus
Belarus
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