Abstract 

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This is a report based on a joint work with Minamoto.  In this talk, we will show 

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a rather surprising result that every AS-regular algebra is graded Morita equivalent 

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to a tensor algebra.  Further, by extending the notion of AS-regularity to 

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non-connected graded algebras, we will show that the classification of AS-regular 

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algebras, that of preprojective algebras, and that of Fano algebras are closely related.

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Since the last two classes of algebras have been intensively studied in representation 

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theory of algebras, this result provides an interesting bridge between noncommutative

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algebraic geometry and representation theory of algebras. If time permits, we will also 

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show that similar results hold for graded Frobenius algebras.