Representations of twisted tensor products of Hopf and Frobenius algebras with a view toward cohomological support

• Project/Area Number: 25K17242
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 11010:Algebra-related
• Research Institution: Okinawa Institute of Science and Technology Graduate University
• Principal Investigator: SANCHEZ・OCAL Pablo 沖縄科学技術大学院大学, 表現論と代数的組合せ論ユニット, ポストドクトラルスカラー (81013183)
• Project Period (FY): 2025-04-01 – 2027-03-31
• Project Status: Granted (Fiscal Year 2025)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2026: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000); Fiscal Year 2025: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
• Keywords: twisted tensor product / Hochschild cohomology / Balmer spectrum / finite tensor category

Outline of Research at the Start

The main goals of this project are to determine necessary and sufficient conditions for when twisted tensor products inherit a Frobenius algebra structure, and to use this characterization to reconstruct certain topological and algebraic information about them. Ultimately, this project aims to employ twisted tensor products to make progress toward Etingof and Ostrik's finite generation conjecture. This will be done using a combination of categorical and (co)homological methods.