Related papers: Pseudo-euclidean Jordan algebras
We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras (EJAs), satisfying some reasonable additional constraints motivated by the desire to construct dagger-compact categories of such…
Aperiodic algebras are infinite dimensional algebras with generators corresponding to an element of the aperiodic set. These algebras proved to be an useful tool in studying elementary excitations that can propagate in multilayered…
We are concerned with the question when Hom-Lie structures on a Lie algebra are closed with respect to the Jordan product. Somewhat unexpectedly, this leads us to certain questions connected with the Yang-Baxter equation, and with…
The contraction and Jordan-Schwinger construction connect the $su(2)$ and the heisenberg algebra, going in oposite directions. This persists in the q-deformed cases, but in a slightly different way. This work investigates this further,…
For every field $F$ which has a quadratic extension $E$ we show there are non-metabelian infinite-dimensional thin graded Lie algebras all of whose homogeneous components, except the second one, have dimension $2$. We construct such Lie…
A celebrated result of Koecher and Vinberg asserts the one-one correspondence between the finite dimensional formally real Jordan algebras and Euclidean symmetric cones. We extend this result to the infinite dimensional setting.
For all three--dimensional Lie algebras the construction of generators in terms of functions on 4-dimensional real phase space is given with a realization of the Lie product in terms of Poisson brackets. This is the classical…
Consider the spaces of pseudodifferential operators between tensor density modules over the line as modules of the Lie algebra of vector fields on the line. We compute the equivalence classes of various subquotients of these modules. There…
We study linear spaces of symmetric matrices whose reciprocal is also a linear space. These are Jordan algebras. We classify such algebras in low dimensions, and we study the associated Jordan loci in the Grassmannian.
A simple unifying view of the exceptional Lie algebras is presented. The underlying Jordan pair content and role are exhibited. Each algebra contains three Jordan pairs sharing the same Lie algebra of automorphisms and the same external…
This paper investigates the Jordan--Kronecker invariant of finite dimensional complex Lie algebras. We present an explicit algorithm for determining the type of a given Lie algebra from its Jordan--Kronecker invariant. The algorithm is…
We discuss quantum deformations of Jordanian type for Lie superalgebras. These deformations are described by twisting functions with support from Borel subalgebras and they are multiparameter in the general case. The total twists are…
A noncommutative Jordan algebra of a specific type is attached to any (-1,-1)-balanced Freudenthal Kantor triple system, in such a way that the triple product in this system is determined by the binary product in the algebra. Over fields of…
Axial algebras of Jordan type $\eta$ are commutative algebras generated by idempotents whose adjoint operators have the minimal polynomial dividing $(x-1)x(x-\eta)$, where $\eta\not\in\{0,1\}$ is fixed, with restrictive multiplication…
We address a Jordan version of Johnson theorem on (associative) algebras of quotients, namely whether a strongly nonsingular (the Jordan version of nonsingularity) has a von Neumann regular algebra of quotients. Although the answer is…
We consider generalization of wellknown construction Kantor Double J({\Gamma}, {,}) (KKM Double, Kantor-King-McCrimmon Double), where basic algebra {\Gamma} is nonunital algebra. We find necessary and sufficient conditions for a generalized…
Recently Jenei introduced a new structure called equality algebras which is inspired by ideas of BCK-algebras with meet. These algebras were generalized by Jenei and K\'or\'odi to pseudo equality algebras which are aimed to find a…
This paper completes description of categories of representations of finite-dimensional simple unital Jordan superalgebras over algebraically closed field of characteristic zero.
We present new results about Jordan algebras and Jordan coalgebras, and we discuss about their connections with the Yang-Baxter equations.
An axial algebra over the field $\mathbb F$ is a commutative algebra generated by idempotents whose adjoint action has multiplicity-free minimal polynomial. For semisimple associative algebras this leads to sums of copies of $\mathbb F$.…