Abstract
Given a nilpotent Lie algebra $L$ of dimension $\le 6$ on an arbitrary field of characteristic $\neq 2$, we show a direct method which allows us to detect the capability of $L$ via computations on the size of its nonabelian exterior square $L \wedge L$. For dimensions higher than $ 6$, we show a result of general nature, based on the evidences of the low dimensional case, focusing on generalized Heisenberg algebras. Indeed we detect the capability of $L \wedge L$ via the size of the Schur multiplier $M(L/Z^\wedge(L))$ of $L/Z^\wedge(L)$, where $Z^\wedge(L)$ denotes the exterior center of $L$.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
