My main research areas are brace theory and pre-lie algebra theory. I am open to expanding my research interests to other topics in algebra as well as topics beyond algebra.

Papers and preprints

Some Braces of Cardinality p^{4} and Related Hopf-Galois Extensions

New York Journal of Mathematics (2022)

Authors: D. Puljić, A. Smoktunowicz, K. Nejabati Zenouz

Abstract: We describe all F_{p}-braces of cardinality p^{4} which are not right nilpotent. Our solution illustrates a general way of investigating F_{p}-braces of cardinality p^{n} 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 p^{4}

Preprint (2022)

Authors: D. Puljić

Abstract: We determine right nilpotency of braces of cardinality p^{4}. If a brace of cardinality p^{4} 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 p^{4}

Preprint (2022)

Authors: D. Puljić

Abstract: We classify nilpotent pre-Lie rings of cardinality p^{4} and thereby braces of the same cardinality, for a sufficiently large prime p. It has been shown that nilpotent pre-Lie rings of cardinality p^{n} 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 p^{4} have been classified, hence our results finish the classification of braces of cardinality p^{4}.

A construction of deformations to general algebras

Preprint (2023)

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.