1 results
K1(
) and the group of automorphisms of the algebra 
of one-sided inverses of a polynomial algebra in two variables
- Part of
-
- Journal:
- Journal of K-Theory / Volume 10 / Issue 3 / December 2012
- Published online by Cambridge University Press:
- 24 May 2012, pp. 583-601
- Print publication:
- December 2012
-
- Article
- Export citation
-
Explicit generators are found for the group G2 of automorphisms of the algebra
of one-sided inverses of a polynomial algebra in two variables over a field. Moreover, it is proved that
where S2 is the symmetric group,
is the 2-dimensional algebraic torus, E∞() is the subgroup of GL∞() generated by the elementary matrices. In the proof, we use and prove several results on the index of an operator. The final argument is the proof of the fact that K1() ≃ K*. The algebras and are noncommutative, non-Noetherian, and not domains.
) and the group of automorphisms of the algebra 
of one-sided inverses of a polynomial algebra in two variables
is the 2-dimensional algebraic torus, 