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We show that there exist some intimate connections between three unconventional Schr\"odinger equations based on the use of deformed canonical commutation relations, of a position-dependent effective mass or of a curved space, respectively.…

In [5] the author conjectures and partially shows that the Cuntz semigroup classifies unitary elements of unital AF-algebras. We provide a complete proof by addressing the existence part of the conjecture, under a mild adjustment of both…

We study the effect of linear duality on action bialgebroids (also known as smash product or scalar extension bialgebroids) and, for those bearing a quantisation nature, the effect of Drinfeld functors underlying the quantum duality…

Observable properties of a classical physical system can be modelled deterministically as functions from the space of pure states to outcomes; dually, states can be modelled as functions from the algebra of observables to outcomes. The…

The standard generators of tridiagonal algebras, recently introduced by Terwilliger, are shown to generate a new (in)finite family of mutually commuting operators which extends the Dolan-Grady construction. The involution property relies on…

We compare the so-called clock condition to the gradability of certain differential modules over quadratic monomial algebras. For a stably hereditary algebra or a gentle one-cycle algebra, these considerations show that the orbit category…

This book is an introductory course to basic commutative algebra with a particular emphasis on finitely generated projective modules, which constitutes the algebraic version of the vector bundles in differential geometry. We adopt the…

The mathematical formalism for linear quantum field theory on curved spacetime depends in an essential way on the assumption of global hyperbolicity. Physically, what lie at the foundation of any formalism for quantization in curved…

We study hom-associative structures on general possibly non-associative algebras focusing on one-sided and two-sided unital algebras. New characterizations and aspects of these structures, along with some important subclasses, are explored…

The partition algebras are algebras of diagrams (which contain the group algebra of the symmetric group and the Brauer algebra) such that the multiplication is given by a combinatorial rule and such that the structure constants of the…

We study maps preserving the Heisenberg commutation relation $ab - ba=1$. We find a one-parameter deformation of the standard realization of the above algebra in terms of a coordinate and its dual derivative. It involves a non-local…

There is a relatively well-known description of the algebra of (higher order) left differential operators on commutative algebras. This note gives a construction of similar flavor for algebras of differential operators on not necessarily…

Consider an algorithm computing in a differential field with several commuting derivations such that the only operations it performs with the elements of the field are arithmetic operations, differentiation, and zero testing. We show that,…

The relation between nonlinear algebras and linear ones is established. For one-dimensional nonlinear deformed Heisenberg algebra with two operators we find the function of deformation for which this nonlinear algebra can be transformed to…

For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…

A method is discussed to analyze the dynamics of a dissipative quantum system. The method hinges upon the definition of an alternative (time-dependent) product among the observables of the system. In the long time limit this yields a…

Let $R$ denote a 2-fir. The notions of F-independence and algebraic subsets of R are defined. The decomposition of an algebraic subset into similarity classes gives a simple way of translating the F-independence in terms of dimension of…

The technique developed in Hochschild's works "Lie algebra kernels and cohomology " and "Cohomology classes of finite dimensional kernels for Lie algebras " [2],[3] can be applied to the special case of transitive Lie algebroids. Our task…

We consider a finite group acting on a vector space and the corresponding skew group algebra generated by the group and the symmetric algebra of the space. This skew group algebra illuminates the resulting orbifold and serves as a…

A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…