A skew Calabi-Yau algebra is a generalization of a Calabi-Yau algebra which allows for a non-trivial Nakayama automorphism. We prove three homological identities about the Nakayama automorphism and give several applications. The identities we prove show (i) how the Nakayama automorphism of a smash product algebra A#H is related to the Nakayama automorphisms of a graded skew Calabi-Yau algebra A...

If φ is an analytic selfmap of the disk (not an elliptic automorphism) the DenjoyWolff Theorem predicts the existence of a point p with |p| ≤ 1 such that the iterates φn converge to p uniformly on compact subsets of the disk. Since these iterates are bounded analytic functions, there is a subset of the unit circle of full linear measure where they are all well-defined. We address the question o...

We extend the Larson–Sweedler theorem for weak Hopf algebras by proving that a finite dimensional weak bialgebra is a weak Hopf algebra iff it possesses a non-degenerate left integral. We establish the autonomous monoidal category of the modules of a weak Hopf algebra A and show the semisimplicity of the unit and the invertible modules of A. We also reveal the connection of these modules to lef...

Let H be a torsion-free δ-hyperbolic group with respect to a finite generating set S. Let g1, . . . , gn and g1∗, . . . , gn∗ be elements of H such that gr∗ is conjugate to gr for each r = 1, . . . , n. There is a uniform conjugator if and only if W (g1∗, . . . , gn∗) is conjugate to W (g1, . . . , gn) for every word W in n variables and length up to a computable constant depending only on δ, ♯...

Let D be a symmetric 2-(121, 16, 2) design with the automorphism group of Aut(D). In this paper the order of automorphism of prime order of Aut(D) is studied, and some results are obtained about the number of fixed points of these automorphisms. Also we will show that |Aut(D)|=2p 3q 5r 7s 11t 13u, where p, q, r, s, t and u are non-negative integers such that r, s, t, u ? 1. In addition we prese...

We relate the character theory of symmetric groups S2n and S2n+1 with that hyperoctahedral group Bn=(Z/2)n⋊Sn, as part expectation reductive diagram automorphism their Weyl groups, is related to fixed subgroup automorphism.

Let G be a countable abelian group. We construct a unital simple projectionless C∗-algebra A with a unique tracial state, that satisfies (K0(A), [1A]) ∼= (Z, 1), K1(A) ∼= G, A ⊗ Z ∼= A, and that is obtained as the inductive limit C∗-algebra of a sequence of dimension drop algebras of a specific form. This construction is based on the construction of the Jiang-Su algebra. By this construction, w...

We investigate the inteplay between the algebraic structure of a group G and arithmetic properties of its spectrum σ(G) which consists of the eigenvalues of all the inner automorphisms of G. A complex number λ is called an eigenvalue of a group automorphism A : G → G if φ ◦ A|H = λ · φ for some non-trivial homomorphism φ : H → C defined on an A-invariant subgroup H ⊂ G. It is shown that many pr...

We introduce a version of Voiculescu-Brown approximation entropy for isometric automorphisms of Banach spaces and develop within this framework the connection between dynamics and the local theory of Banach spaces as discovered by Glasner and Weiss. Our fundamental result concerning this contractive approximation entropy, or CA entropy, characterizes the occurrence of positive values both geome...

In this paper, we will determine the full automorphism groups of rose window graphs that are not edge-transitive. As the full automorphism groups of edge-transitive rose window graphs have been determined, this will complete the problem of calculating the full automorphism group of rose window graphs. As a corollary, we determine which rose window graphs are vertex-transitive. Finally, we deter...