Abstract. Newman, Schneider and Shalev defined the entropy of a graded associative algebra A as H(A) = lim sup n→∞ n √ an, where an is the vector space dimension of the n’th homogeneous component. When A is the homogeneous quotient of a finitely generated free associative algebra, they showed that H(A) ≤ √ a2. Using some results of Friedland on the maximal spectral radius of (0, 1)-matrices wit...

The present paper addresses the problem of attainment of the supremums in various equivalent definitions of hereditary density hd and hereditary Lindelöf degree hL of Boolean algebras. We partially answer two problems of J. Donald Monk, [13, Problems 50, 54], showing consistency of different attainment behaviour and proving that (for the considered variants) this is the best result we can expec...

Some Lie algebra analogues of Schur's theorem and its converses are presented. As a result, it is shown that for a capable Lie algebra L we always have dim L=Z(L) 2(dim(L2))2. We also give give some examples sup- porting our results.

We investigate the relation between supersymmetry and geometry for two dimensional sigma models with target spaces of arbitrary signature, and Lorentzian or Euclidean world-sheets. In particular, we consider twisted forms of the two-dimensional (p, q) supersymmetry algebra. Superspace formulations of the (p, q) heterotic sigma-models with twisted or untwisted supersymmetry are given. For the tw...

We derive the classical algebra of the non-local conserved charges in the O(N) WZNW model and analyze its dependence on the coupling constant of the Wess-Zumino term. As in the non-linear sigma model, we find cubic deformations of the O(N) affine algebra. The surprising result is that the cubic algebra of the WZNW non-local charges does not obey the Jacobi identity, thus opposing our expectatio...

We identify a simple mechanism by which H-flux satisfying the modified Bianchi identity arises in garden-variety (0, 2) gauged linear sigma models. Taking suitable limits leads to effective gauged linear sigma models with Green-Schwarz anomaly cancellation. We test the quantumconsistency of a class of such effective theories by constructing an off-shell superconformal algebra, identifying unexp...

We find a new class of (2,0)-supersymmetric two-dimensional sigma models with torsion and target spaces almost complex manifolds extending similar results for models with (2,2) supersymmetry. These models are invariant under a new symmetry which is generated by a Noether charge of Lorentz weight one and it is associated to the Nijenhuis tensor of the almost complex structure of the sigma model ...

Based on the notion of $Q$-sup-lattices (a fuzzy counterpart of complete join-semilattices valuated in a commutative quantale), we present the concept of $Q$-sup-algebras -- $Q$-sup-lattices endowed with a collection of finitary operations compatible with the fuzzy joins. Similarly to the crisp case investigated in cite{zhang-laan}, we characterize their subalgebras and quotients, and following...