Date of Award
Doctor of Philosophy (PhD)
Commutative algebra, Grobner Shirshov basis, Hochschild cohomology, Koszul algebra
Mathematics | Physical Sciences and Mathematics
Let k be a field of characteristic 0. In this thesis, we show that the Hochschild cohomology of the family of short Gorenstein k-algebras
sGor(N) =k[X_0,...,X_N](X_iX_j, X_i^2−X_j^2 | i,j= 0,...,N, i different from j), N≥2,
exhibits exponential growth. The proof uses Gröbner-Shirshov basis theory and along the way we describe an explicit monomial basis for the Koszul dual of sGor(N) for N≥2.
Ohanyan, Mkrtich, "Hochschild Cohomology of Short Gorenstein Rings" (2021). Dissertations - ALL. 1364.