Gendo-symmetric algebras, canonical comultiplication, bar cocomplex and dominant dimension

Fang, Ming; Koenig, Steffen

doi:10.1090/tran/6504

Gendo-symmetric algebras, canonical comultiplication, bar cocomplex and dominant dimension
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Trans. Amer. Math. Soc. 368 (2016), 5037-5055 Request permission

Abstract:

To each endomorphism algebra $A$ of a generator over a symmetric algebra, first a canonical comultiplication (possibly without a counit) is constructed and then a bar cocomplex. The algebras $A$ are characterised by the existence of this data. The dominant dimension of $A$ is shown to be determined by the exactness of the cocomplex at its beginning terms.

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