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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Deformations of finite-dimensional algebras and their idempotents


Author: M. Schaps
Journal: Trans. Amer. Math. Soc. 307 (1988), 843-856
MSC: Primary 16A46; Secondary 16A58
MathSciNet review: 940231
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Abstract: Let $ B$ be a finite dimensional algebra over an algebraically closed field $ K$. If we represent primitive idempotents by points and basis vectors in $ {e_i}B{e_j}$ by "arrows" from $ {e_j}$ to $ {e_i}$, then any specialization of the algebra acts on this directed graph by coalescing points. This implies that the number of irreducible components in the scheme parametrizing $ n$-dimensional algebras is no less than the number of loopless directed graphs with a total of $ n$ vertices and arrows. We also show that the condition of having a distributive ideal lattice is open.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1988-0940231-4
PII: S 0002-9947(1988)0940231-4
Article copyright: © Copyright 1988 American Mathematical Society