V. N. Zhelyabin | Searcharxiv

arXiv2010

New Examples of Simple Jordan Superalgebras over an Arbitrary Field of Characteristic Zero

I.P. Shestakov constructed an example of a unital simple special Jordan superalgebra over the field of real numbers. It turned out to be a subsuperalgebra of the Jordan superalgebra of vector type, but not isomorphic to a superalgebra of this type. Moreover, its superalgebra of fractions is isomorphic to a Jordan superalgebra of vector type. Author constructed a similar example of a Jordan superalgebra over a field of characteristic~0 in which the equation $t^2+1=0$. In this article we present an~example of a Jordan superalgebra with the same properties over an arbitrary field of characteristic 0. A similar example of a superalgebra is found in the Cheng-Kac superalgebra.

math.RA↗

arXiv2010

The Kantor-Koecher-Tits Construction for Jordan Coalgebras

The relationship between Jordan and Lie coalgebras is established. We prove that from any Jordan coalgebra $\langle A, Δ\rangle$, it is possible to construct a Lie coalgebra $\langle L(A), Δ_{L}\rangle$. Moreover, any dual algebra of the coalgebra $\langle L(A), Δ_{L}\rangle$ corresponds to a Lie algebra that can be determined from the dual algebra for $\langle A,Δ\rangle$, following the Kantor--Koecher--Tits process. The structure of subcoalgebras and coideals of the coalgebra $\langle L(A), Δ_{L}\rangle$ is characterized.

math.RA↗