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We study the Riesz Decomposition Property types of the lexicographic product of two po-groups. Then we apply them to the study of pseudo effect algebras which can be decomposed to a comparable system of non-void slices indexed by some subgroup of real numbers. Finally, we present their representation by the lexicographic product.
We suggest the notion of perfect integrability for quantum spin chains and conjecture that quantum spin chains are perfectly integrable. We show the perfect integrability for Gaudin models associated to simple Lie algebras of all finite types, with p
Analytic mass-spring chains with dispersionless pulse transfer and fractional revival are presented. These are obtained using the properties of the para-Racah polynomials. This provides classical analogs of the quantum spin chains that realize import
In Section 1 we review various equivalent definitions of a vertex algebra V. The main novelty here is the definition in terms of an indefinite integral of the lambda-bracket. In Section 2 we construct, in the most general framework, the Zhu algebra Z
The notion of $Gamma$-symmetric space is a natural generalization of the classical notion of symmetric space based on $z_2$-grading of Lie algebras. In our case, we consider homogeneous spaces $G/H$ such that the Lie algebra $g$ of $G$ admits a $Gamm
We obtain certain Mellin-Barnes integrals which present wave functions for $GL(n,mathbb{R})$ hyperbolic Sutherland model with arbitrary positive coupling constant.