Hochschild and cyclic homology of 3-preprojective algebras of type A

Morigi, Davide (2022) Hochschild and cyclic homology of 3-preprojective algebras of type A. Doctoral thesis, University of East Anglia.

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The subjects of study of this thesis are 3-preprojective algebras II of type A, a higher generalisation of classical preprojective algebras of type A in the sense of Iyama. These algebras enjoy many nice homological properties: they are Frobenius, almost Koszul and (twisted) periodic. They can be described in terms of quivers with relations, which makes computations easier to perform.
In this thesis, we use the aforementioned properties to give a conjectural description of the Hochschild homology, cohomology and cyclic homology groups of these algebras. The conjectural part depends on the truthfulness of a formula that allows us to compute the cyclic homology in terms of the determinant of the Hilbert series of II, and on the computation of the determinant of a matrix with polynomial entries, that we verify with the use of GAP [32] for the first 30 cases.

Item Type: Thesis (Doctoral)
Faculty \ School: Faculty of Science > School of Mathematics
Depositing User: Kitty Laine
Date Deposited: 27 Jun 2023 12:20
Last Modified: 27 Jun 2023 12:20
URI: https://ueaeprints.uea.ac.uk/id/eprint/92512

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