Related papers: On neat atom structures for cylindric like algebra…
It is shown that if a C*-algebra has nuclear dimension $n$ then its Cuntz semigroup has the property of $n$-comparison. It then follows from results by Ortega, Perera, and Rordam that $\sigma$-unital C*-algebras of finite nuclear dimension…
We study classes of atomic models At_T of a countable, complete first-order theory T . We prove that if At_T is not pcl-small, i.e., there is an atomic model N that realizes uncountably many types over pcl(a) for some finite tuple a from N,…
Let p be prime number, K be a p-adically closed field, X $\subseteq$ K^m a semi-algebraic set defined over K and L(X) the lattice of semi-algebraic subsets of X which are closed in X. We prove that the complete theory of L(X) eliminates the…
We show that, up to terms of order 1/kappa^5, the kappa-deformed Poincare algebra can be endowed with a triangular quasibialgebra structure. The universal R matrix and coassociator are given explicitly to the first few orders. In the…
We develop an elementary formula for certain non-trivial elements of upper cluster algebras. These elements have positive coefficients. We show that when the cluster algebra is acyclic these elements form a basis. Using this formula, we…
The structure of the observable algebra ${\mathfrak O}_{\Lambda}$ of lattice QCD in the Hamiltonian approach is investigated. As was shown earlier, ${\mathfrak O}_{\Lambda}$ is isomorphic to the tensor product of a gluonic…
We study Archimedean atomic lattice effect algebras whose set of sharp elements is a complete lattice. We show properties of centers, compatibility centers and central atoms of such lattice effect algebras. Moreover, we prove that if such…
Lascoux stated that the type A Kostka-Foulkes polynomials K_{lambda,mu}(t) expand positively in terms of so-called atomic polynomials. For any semisimple Lie algebra, the former polynomial is a t-analogue of the multiplicity of the dominant…
A non-associative algebra over a field $\mathbb{K}$ is a $\mathbb{K}$-vector space $A$ equipped with a bilinear operation \[ {A\times A\to A\colon\; (x,y)\mapsto x\cdot y=xy}. \] The collection of all non-associative algebras over…
We introduce the decomposition rank, a notion of covering dimension for nuclear C^*-algebras. The decomposition rank generalizes ordinary covering dimension and has nice permanence properties; in particular, it behaves well with respect to…
We answer an implicit question of Ian Hodkinson's. We show that atomic Pinters algebras may not be completely representable, however the class of completely representable Pinters algebras is elementary and finitely axiomatizable. We obtain…
We give a categorial definition separating cylindric-like algebras from polyadic-like ones. Viewing the neat reduct operator as a functor, we show that it does not have a right adjoint in the former case, but it is strongly invertible in…
The universal-algebraic approach has proved a powerful tool in the study of the complexity of CSPs. This approach has previously been applied to the study of CSPs with finite or (infinite) omega-categorical templates, and relies on two…
The congruence lattices of all algebras defined on a fixed finite set $A$ ordered by inclusion form a finite atomistic lattice $\mathcal E$. We describe the atoms and coatoms. Each meet-irreducible element of $\mathcal E$ being determined…
Motivated by the sharp contrast between classical and quantum physics as probability theories, in these lecture notes I introduce the basic notions of operator algebras that are relevant for the algebraic approach to quantum physics.…
In this article I study a number of topological and algebraic dimension type properties of simple C*-algebras and their interplay. In particular, a simple C*-algebra is defined to be (tracially) (m,\bar{m})-pure, if it has (strong tracial)…
Algebras on the natural numbers and their clones of term operations can be classified according to their descriptive complexity. We give an example of a closed algebra which has only unary operations and whose clone of term operations is…
An algebraic structure is said to be congruence permutable if its arbitrary congruences $\alpha$ and $\beta$ satisfy the equation $\alpha \circ \beta =\beta \circ \alpha$, where $\circ$ denotes the usual composition of binary relations. For…
We use Monk like algebras to give a new proof that the classes of strongly representable relation algebras and finite dimensional cylindric algebras of dimension >2 are not elementary. Our construction is based on relation algebras have…
Clifford algebras are important structures in Geometric Algebra and Quantum Mechanics. They have allowed a formalization of the primitive operators in Quantum Theory. The algebras are built over vector spaces with dimension a power of 2…