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The Sasaki projection was introduced as a mapping from the lattice of closed subspaces of a Hilbert space onto one of its segments. To use this projection and its dual so-called Sasaki operations were introduced by the second two authors.…
We introduce the blockwise gluing construction. This describes residuated integral chains which can be decomposed into (possibly) partial algebras, stacked one on top of the other, and such that elements in a certain component multiply in…
We generalize to the case of Lie superalgebras the classical symplectic double extension of symplectic Lie algebras introduced in [2]. We use this concept to give an inductive description of nilpotent homogeneous-symplectic Lie…
Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…
We introduce labelled sequent calculi for the basic normal non-distributive modal logic L and 31 of its axiomatic extensions, where the labels are atomic formulas of a first order language which is interpreted on the canonical extensions of…
We study the generalization of S-duality to non-commutative gauge theories. For rank one theories, we obtain the leading terms of the dual theory by Legendre transforming the Lagrangian of the non-commutative theory expressed in terms of a…
This is a survey of results on partially commutative groups and partially commutative algebras.
The correspondence between ordinary differential equations and Bethe ansatz equations for integrable lattice models in their continuum limits is generalised to vertex models related to classical simple Lie algebras. New families of…
We describe how the usual supercharges of extended supersymmetry may be {\it twisted} to produce a BRST-like supercharge $Q$. The usual supersymmetry algebra is then replaced by a twisted algebra and the action of the twisted theory is…
We define alternating cyclotomic Hecke algebras in higher levels as subalgebras of cyclotomic Hecke algebras under an analogue of Goldman's hash involution. We compute the rank of these algebras and construct a full set of irreducible…
We illustrate some problems that are related to the existence of an underlying linear structure at the level of the property lattice associated with a physical system, for the particular case of two explicitly separated spin 1/2 objects…
Injectives in several classes of structures associated with logic are characterized. Among the classes considered are residuated lattices, MTL-algebras, IMTL-algebras, BL-algebras, NM-algebras and bounded hoops.
We classify the finite dimensional semi-weight representations of the reduced stated skein algebras at odd roots of unity of connected marked surfaces which either have a boundary component with at least two boundary edges or which do not…
The concept of derivation for Lie-Yamaguti algebras is generalized in this paper. A quasi-derivation of an LY-algebra is embedded as derivation in a larger LY-algebra. The relationship between quasi-derivations and robustness of…
We define the notion of a partially additive Kleene algebra, which is a Kleene algebra where the + operation need only be partially defined. These structures formalize a number of examples that cannot be handled directly by Kleene algebras.…
The concept of a Kleene algebra (sometimes also called Kleene lattice) was already generalized by the first author for non-distributive lattices under the name pseudo-Kleene algebra. We extend these concepts to posets and show how…
For an arbitrary partially ordered set $P$ its {\em dual} $P^*$ is built as the collection of all monotone mappings $P\to\2$ where $\2=\{0,1\}$ with $0<1$. The set of mappings $P^*$ is proved to be a complete lattice with respect to the…
We introduce a sequent calculus FL' for non-commutative substructural logic. It has at most one formula on the right side of sequent, and excludes three structural inference rules, i.e. contraction, weakening and exchange. (FL' is based on…
We give an explicit description of commutative post-Lie algebra structures on some classes of nilpotent Lie algebras. For non-metabelian filiform nilpotent Lie algebras and Lie algebras of strictly upper-triangular matrices we show that all…
This paper is a contribution to the theory of finite semigroups and their classification in pseudovarieties, which is motivated by its connections with computer science. The question addressed is what role can play the consideration of an…