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- W1979288045 abstract "Let K ( X ) be the quotient field of the polynomial ring K [ X ] over an algebraically closed field K . Given an integer n ≥ 2, a finite sequence m = ( m 2 ,…, m n ) of n − 1 positive integers, a sequence α = (α 2 ,…,α n ) of K -linear functionals on K ( X ), and a height function h , there is attached a Kronecker module E = E ( m , h , α ). In this paper we show that when E has no finite-dimensional direct summand then End E is a commutative K -subalgebra of the algebra of n × n matrices over K ( X ). Consequently, when End E is an integral domain its transcendence degree over K is at most one. We give sufficient conditions for End E to be isomorphic to K and also show that K is the only field that occurs as End E . Examples where K [ X ], K [ X , X − 1 ], and some subalgebras of K ( X ) n occur as End E are given. The determination of all the commutative K -subalgebras of M n ( K ( X )) realizable as End E remains open. Yet surprisingly it can be shown that the coordinate ring of a cubic equation in Weierstrass normal form Y 2 = X 3 + aX 2 + bX + c is realizable." @default.
- W1979288045 created "2016-06-24" @default.
- W1979288045 creator A5007025270 @default.
- W1979288045 creator A5045792937 @default.
- W1979288045 date "1998-03-01" @default.
- W1979288045 modified "2023-09-29" @default.
- W1979288045 title "A Family of Commutative Endomorphism Algebras" @default.
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- W1979288045 doi "https://doi.org/10.1006/jabr.1997.7293" @default.
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