ABSTRACT
In this paper we introduce a generalization of the exterior algebra of a vector space V. We study some of its properties and give explicit computations for the case
. In particular we show the existence and uniqueness of a determinant-like function
with the property that
if there exists
such that
. We also introduce the notion of GSC-operads and show how
fits in that context.
2020 MATHEMATICS SUBJECT CLASSIFICATION:
Acknowledgments
We thank Tong Sun for some discussions and help with MATLAB. We thank Alin Stancu and Florin Panaite for comments and discussions. We thank anonymous referees for bringing to our attention connections with projective geometry, reference [Citation21], and for suggestions that helped us improve the presentation.
Data availability statement
The data that support the findings of this study are available from the corresponding author, MS, upon reasonable request.
Disclosure statement
There is no conflict of interest.