Katsylo, Pavel; Mikhailov, Dmitry Ternary quartics and 3-dimensional commutative algebras. (English) Zbl 0910.14011 J. Lie Theory 7, No. 2, 165-169 (1997). A structure of a commutative algebra on \(\mathbb{C}^3\) is called a 3-dimensional algebra. Let \({\mathcal A}\) be the set of 3-dimensional algebras. Consider \({\mathcal A}\) as a linear space. Let \({\mathcal A}_0 \subset {\mathcal A}\) be the linear subspace of algebras with trivial trace. By definition, \(\eta\in {\mathcal A}_0\) if the contraction of the structure tensor of \(\eta\) is equal to zero.In this paper we find a connection between 3-dimensional commutative algebras with trivial trace and plane quartics and their bitangents. Cited in 2 Documents MSC: 14H50 Plane and space curves 15A78 Other algebras built from modules 13C99 Theory of modules and ideals in commutative rings Keywords:3-dimensional commutative algebras; plane quartics PDFBibTeX XMLCite \textit{P. Katsylo} and \textit{D. Mikhailov}, J. Lie Theory 7, No. 2, 165--169 (1997; Zbl 0910.14011) Full Text: arXiv EuDML