Classification of matrix idempotents over a subalgebra of $K[x]$ generated by monomials
Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 201-209
Let $K$ be a commutative integral domain such that all finitely generated projective modules over $K[x]$ are free. Let $\Lambda$ be a subalgebra of $K[x]$ generated by monomials, such that there are only finitely many monomials in $K[x]$ which do not belong to $\Lambda$. For such algebras, the following results are obtained: matrix idempotents over $\Lambda$ are described up to conjugation; provided that $\frac12\in K$, finite-dimensional representations of a group of order 2 over $\Lambda$ are described up to an isomorphism; and all finitely generated projective $\Lambda$-modules are described up to an isomorphism. These results can be generalized to the case of subalgebras of the algebra of polynomials $K[x_1,\dots,X_n]$ with $n>1$. Bibliography: 3 titles.
@article{SM_1988_61_1_a14,
author = {V. V. Plakhotnik},
title = {Classification of matrix idempotents over a~subalgebra of $K[x]$ generated by monomials},
journal = {Sbornik. Mathematics},
pages = {201--209},
year = {1988},
volume = {61},
number = {1},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_1988_61_1_a14/}
}
V. V. Plakhotnik. Classification of matrix idempotents over a subalgebra of $K[x]$ generated by monomials. Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 201-209. http://geodesic.mathdoc.fr/item/SM_1988_61_1_a14/
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