Abstract:We consider the concept of a right representation for Novikov algebras. We introduce the concept of a right modular ideal of a Novikov algebra and obtain a description of irreducible right representations of a Novikov algebra as quotients by maximal modular right ideals.
We prove that the class of Novikov algebras without irreducible representations is a hereditary radical. We introduce the concept of a primitive Novikov algebra and prove that a Novikov algebra is primitive if and only if it has an almost faithful irreducible representation. We introduce the concept of the quasi-kernel of a representation as the largest ideal contained in the kernel of the representation. We prove that the Jacobson radical of a Novikov algebra is the intersection of the quasi-kernels of all irreducible representations of this algebra.
From: Alexander Panasenko [view email]
[v1]
Mon, 15 Jun 2026 09:05:13 UTC (14 KB)
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