Abstract
The Baues–Wirsching cohomology is one of the cohomologies of a small category. Our aim is to describe the first Baues–Wirsching cohomology of the small category generated by a finite quiver freely. We consider the case where the coefficient is a natural system obtained by the composition of a functor and the target functor. We give an algorithm to obtain generators of the vector space of inner derivations. It is known that there exists a surjection from the vector space of derivations of the small category to the first Baues–Wirsching cohomology whose kernel is the vector space of inner derivations.
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References
Baues, H.J., Wirsching, G.: Cohomology of small categories. J. Pure Appl. Algebra 38(2-3), 187–211 (1985)
Buchweitz, R.-O., Green, E.L., Snashall, N., Solberg, Ø.: Multiplicative structures for Koszul algebras. Q. J. Math. 59(4), 441–454 (2008)
Green, E.L., Solberg, Ø.: An algorithmic approach to resolutions. J. Symbolic Comput. 42(11-12), 1012–1033 (2007)
Han, Y.: Hochschild (co)homology dimension. J. London Math. Soc. (2) 73(3), 657–668 (2006)
Mitchell, B.: Rings with several objects. Advances in Math. 8, 1–161 (1972)
Momose, Y., Numata, Y.: On the Baues–Wirsching cohomology of B 2-free posets (in preparation)
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Momose, Y., Numata, Y. (2014). On Computation of the First Baues–Wirsching Cohomology of a Freely-Generated Small Category. In: Hong, H., Yap, C. (eds) Mathematical Software – ICMS 2014. ICMS 2014. Lecture Notes in Computer Science, vol 8592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44199-2_17
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DOI: https://doi.org/10.1007/978-3-662-44199-2_17
Publisher Name: Springer, Berlin, Heidelberg
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