A family of Koszul self-injective algebras with finite Hochschild cohomology

This paper presents an infinite family of Koszul self-injective algebras whose Hochschild cohomology ring is finite-dimensional. Moreover, for each $N \geq 5$ we give an example where the Hochschild cohomology ring has dimension $N$. This family of algebras includes and generalizes the 4-dimensional Koszul self-injective local algebras of Buchweitz, Green, Madsen and Solberg, which were used to give a negative answer to Happel's question, in that they have infinite global dimension but finite-dimensional Hochschild cohomology.Comment: 17 page

The Ext algebra and a new generalisation of D-Koszul algebras

We generalise Koszul and D-Koszul algebras by introducing a class of graded algebras called (D,A)-stacked algebras. We give a characterisation of (D,A)-stacked algebras and show that their Ext algebra is finitely generated as an algebra in degrees 0, 1, 2 and 3. In the monomial case, we give an explicit description of the Ext algebra by quiver and relations, and show that the ideal of relations has a quadratic Gr\"obner basis; this enables us to give a regrading of the Ext algebra under which the regraded Ext algebra is a Koszul algebra.Comment: New title; minor changes; 25 page

Group actions and coverings of Brauer graph algebras

We develop a theory of group actions and coverings on Brauer graphs that parallels the theory of group actions and coverings of algebras. In particular, we show that any Brauer graph can be covered by a tower of coverings of Brauer graphs such that the topmost covering has multiplicity function identically one, no loops, and no multiple edges. Furthermore, we classify the coverings of Brauer graph algebras that are again Brauer graph algebras.Comment: 26 pages Correction to statement of Theorem 6.7; a tower of coverings has been introduce

The idea of residence in the neolithic Cotswolds.

This thesis is an investigation of the idea of residence in the British Neolithic carried out at a regional level. The aim is to produce a clearer understanding of ideas and modes of residence as experienced by groups residing in the Cotswolds between the Later Mesolithic and the Early Bronze Age. This is undertaken through the use of lithic assemblages in combination with other sources of monumental and topographical information. The assemblages are analysed in a series of sampling units chosen to reflect the diversity in monumentality and topography within the region. Analysis of the assemblages is undertaken in two stages. The first establishes the validity of using Pitts’ and Jacobi’s (1979) chronometric methodology within the region and goes on to suggest a supplementary method more suited to dealing with lithic material produced within a parsimonious tradition of stone working. The second stage builds upon the chronometric patterning established in the first phase. It uses this patterning in combination with a technological and typological analysis of selected assemblages to establish the residential choices made by communities in different topographic and monumental areas. The analyses of the character of individual assemblages is then used to build an understanding of the residential choices made in different periods within individual monumental and topographical areas. Finally an attempt is made to draw out the contrasts and continuities in residential practices in the region as a whole during different periods

Hochschild cohomology of socle deformations of a class of Koszul self-injective algebras

We consider the socle deformations arising from formal deformations of a class of Koszul self-injective special biserial algebras which occur in the study of the Drinfeld double of the generalized Taft algebras. We show, for these deformations, that the Hochschild cohomology ring modulo nilpotence is a finitely generated commutative algebra of Krull dimension 2.Comment: 10 pages. Minor changes, references updated. To appear in Colloq. Math