{"id":{"repo_id":"syracuse-diss","oai_identifier":"oai:surface.syr.edu:etd-2325"},"canonical_url":"https://search.dev.ndltd.org/etd/syracuse-diss/oai:surface.syr.edu:etd-2325","repository":{"repo_id":"syracuse-diss","name":"Syracuse University","base_url":"https://surface.syr.edu/do/oai/"},"display":{"title":"Hochschild Cohomology Of Short Gorenstein Rings","abstract":"<p>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 </p><p>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,</p><p>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.</p>","abstract_html":"&lt;p&gt;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 &lt;/p&gt;&lt;p&gt;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,&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;","abstract_has_math":false,"creators":["Ohanyan, Mkrtich"],"institution":null,"degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Claudia Miller","Benjamin Briggs"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2021,"date_issued":"2021-05-22T07:00:00Z","date_published":"2021-05-22T07:00:00Z","updated_at":"2026-07-24T04:56:04Z","subjects":["Commutative algebra","Grobner Shirshov basis","Hochschild cohomology","Koszul algebra","Physical Sciences and Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://surface.syr.edu/etd/1324","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Claudia Miller","Benjamin Briggs"]},{"key":"dc:creator","label":"Author","values":["Ohanyan, Mkrtich"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Commutative algebra","Grobner Shirshov basis","Hochschild cohomology","Koszul algebra","Physical Sciences and Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://surface.syr.edu/etd/1324"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["<p>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 </p><p>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,</p><p>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.</p>"]},{"key":"dc:title","label":"Title","values":["Hochschild Cohomology Of Short Gorenstein Rings"]}]}],"canonical_facts":{"dc:contributor":["Claudia Miller","Benjamin Briggs"],"dc:creator":["Ohanyan, Mkrtich"],"dc:description.abstract":["<p>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 </p><p>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,</p><p>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.</p>"],"dc:identifier":["https://surface.syr.edu/etd/1324"],"dc:subject":["Commutative algebra","Grobner Shirshov basis","Hochschild cohomology","Koszul algebra","Physical Sciences and Mathematics"],"dc:title":["Hochschild Cohomology Of Short Gorenstein Rings"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"]},"updated_at":"2026-07-24T04:56:04Z"}