My main research areas are brace theory and pre-lie algebra theory. My PhD thesis achieves the classification of braces of cardinality p4.
Papers and preprints
Some Braces of Cardinality p4 and Related Hopf-Galois Extensions
New York Journal of Mathematics (2022)
Authors: D. Puljić, A. Smoktunowicz, K. Nejabati Zenouz
Abstract: We describe all Fp-braces of cardinality p4 which are not right nilpotent. Our solution illustrates a general way of investigating Fp-braces of cardinality pn with a given multiplicative group. The constructed braces are left nilpotent, solvable and prime, and they also contain a non-zero strongly nilpotent ideal.
Right Nilpotency of Braces of Cardinality p4
Preprint (2022)
Authors: D. Puljić
Abstract: We determine right nilpotency of braces of cardinality p4. If a brace of cardinality p4 has an abelian multiplicative group, then it is left and right nilpotent, so we only consider braces with non-abelian multiplicative groups. We show right nilpotency in all cases using the sufficient condition of A∗c=0 for some central element c of a brace A.
Classification of braces of cardinality p4
Journal of Algebra (2024)
Authors: D. Puljić
Abstract: We classify nilpotent pre-Lie rings of cardinality p4 and thereby braces of the same cardinality, for a sufficiently large prime p. It has been shown that nilpotent pre-Lie rings of cardinality pn correspond to strongly nilpotent braces of the same cardinality, for sufficiently large p. These braces are explicitly obtained from the corresponding pre-Lie rings by the construction of the group of flows. Not right nilpotent braces of cardinality p4 have been classified, hence our results finish the classification of braces of cardinality p4.
A construction of deformations to general algebras
International Mathematics Research Notices (2024)
Authors: D. Bowman, D. Puljić, A. Smoktunowicz
Abstract: One of the questions investigated in deformation theory is to determine to which algebras can a given associative algebra be deformed. In this paper we investigate a different but related question, namely: for a given associative finite-dimensional C-algebra A, find algebras N which can be deformed to A. We develop a simple method which produces associative and flat deformations to investigate this question. As an application of this method we answer a question of Michael Wemyss about deformations of contraction algebras.