论文标题
nilpotent diassociative代数的乘数
Multipliers of Nilpotent Diassociative Algebras
论文作者
论文摘要
该论文涉及Nilpotent的关联拨号桥及其相应的DIASSsosiative Schur乘数。使用谎言（和群体）理论作为指导，我们首先在替代条件下在替代条件下延伸了经典的五项同胞序列。然后将此主要结果应用于获得同一序列的先前扩展的新证明。它还产生了涉及上央序列中术语的序列的不同扩展。此外，我们使用主要结果来获得nilpotent Diassociative代数的乘数上的维度界限的集合。这些不同于谎言案。由于DIASSsopiative代数概括了联想代数，因此我们获得了此处结果的关联类似物。我们通过计算关联代数的关联和二心乘积乘数来结束。本文是一个正在进行的项目的一部分，该项目旨在在几个Loday代数的背景下推进扩展理论。
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.
