2022/02/15 by Erik Mainellis, Mainellis, Erik
Mathematics · #17A30 #19C09 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.RA #msc:17A30 #msc:19C09
paper · pdf · doi:10.48550/arxiv.2202.07563
12 pages
arxiv created 2022/02/15 · openalex publication_date 2022/02/15 · arxiv updated 2022/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The paper concerns nilpotent associative dialgebras and their corresponding diassociative Schur multipliers. Using Lie (and group) theory as a guide, we first extend a classic five-term cohomological sequence under alternative conditions in the nilpotent setting. This main result is then applied to obtain a new proof for a previous extension of the same sequence. It also yields a different extension of the sequence that involves terms in the upper central series. Furthermore, we use the main result to obtain a collection of dimension bounds on the multiplier of a nilpotent diassociative algebra. These differ notably from the Lie case. Since diassociative algebras generalize associative algebras, we obtain an associative analogue of the results herein. We conclude by computing both the associative and diassociative multipliers of an associative algebra. This paper is part of an ongoing project to advance extension theory in the context of several Loday algebras.