论文标题
乘数和完美的Diassociative代数的封面
Multipliers and Covers of Perfect Diassociative Algebras
论文作者
论文摘要
该论文涉及完美的DIASSSSSsopiative代数及其对中央扩展理论的影响。首先确定完美的DIASSSSSOCIATIVE代数与通用中央扩展具有牢固的联系。然后，使用自由演示的乘数对乘数的已知表征，我们获得了完美的DiaSssociative代数及其某些特性的特殊封面。随后的结果连接并建立在先前的主题上。对于最终定理，我们调用了扩展的Hochschild-Serre型光谱序列，以表明，对于完美的Diassociative代数，其封面是完美的，并且具有微不足道的乘数。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 perfect diassociative algebras and their implications to the theory of central extensions. It is first established that perfect diassociative algebras have strong ties with universal central extensions. Then, using a known characterization of the multiplier in terms of a free presentation, we obtain a special cover for perfect diassociative algebras, as well as some of its properties. The subsequent results connect and build on the previous topics. For the final theorem, we invoke an extended Hochschild-Serre type spectral sequence to show that, for a perfect diassociative algebra, its cover is perfect and has trivial multiplier. This paper is part of an ongoing project to advance extension theory in the context of several Loday algebras.
