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

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- by Ming Fang and Steffen Koenig PDF
- 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.## References

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## Additional Information

**Ming Fang**- Affiliation: Institute of Mathematics, Chinese Academy of Sciences Beijing 100190, People’s Republic of China
- MR Author ID: 715486
- Email: fming@amss.ac.cn
**Steffen Koenig**- Affiliation: Institute of Algebra and Number Theory, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
- MR Author ID: 263193
- Email: skoenig@mathematik.uni-stuttgart.de
- Received by editor(s): January 22, 2014
- Received by editor(s) in revised form: June 4, 2014
- Published electronically: October 5, 2015
- Additional Notes: The first author was supported by the National Natural Science Foundation of China (No.11001253 and No. 11271318)
- © Copyright 2015 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**368**(2016), 5037-5055 - MSC (2010): Primary 16G10, 13E10
- DOI: https://doi.org/10.1090/tran/6504
- MathSciNet review: 3456170