Orbit algebras and periodicity
نویسندگان
چکیده
منابع مشابه
Orbit Algebras and Periodicity
Given an object in a category, we study its orbit algebra with respect to an endofunctor. We show that if the object is periodic, then its orbit algebra modulo nilpotence is a polynomial ring in one variable. This specializes to a result on Ext-algebras of periodic modules over Gorenstein algebras. We also obtain a criterion for an algebra to be of wild representation
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Kumjian and Pask introduced an aperiodicity condition for higher rank graphs. We present a detailed analysis of when this occurs in certain rank 2 graphs. When the algebra is aperiodic, we give another proof of the simplicity of C(Fθ ). The periodic C*algebras are characterized, and it is shown that C(Fθ ) ' C(T)⊗A where A is a simple C*-algebra.
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We show that for piecewise hereditary algebras, the periodicity of the Coxeter transformation implies the nonnegativity of the Euler form. Contrary to previous assumptions, the condition of piecewise heredity cannot be omitted, even for triangular algebras, as demonstrated by incidence algebras of posets. We also find that the only condition on a matrix A needed to express certain products of r...
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ژورنال
عنوان ژورنال: Colloquium Mathematicum
سال: 2009
ISSN: 0010-1354,1730-6302
DOI: 10.4064/cm114-2-7