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In this paper, we construct a symbol calculus yielding short exact sequences for the dual Toeplitz algebra generated by all bounded dual Toeplitz operators on the Hardy space associated with the polydisk D n in the unitary space C n , that have been introduced and well studied in our earlier paper (Benaissa and Guediri in Taiwan J Math 19: 31–49, 2015), as well as for the C*-subalgebra generated by dual Toeplitz operators with symbols continuous on the associated hypertorus T n . [ABSTRACT FROM AUTHOR]

In this paper, approximate Noether and Lie symmetries of 2nd order for Gibbons–Maeda–Garfinkle–Horowitz–Strominger (GMGHS) charged black hole in the Einstein frame are analyzed comprehensively. To explore the approximate Noether symmetries of 2nd order, Noether symmetries of Minkowski spacetime are used which forms a 17 dimensional Lie algebra. It is observed that no new approximate Noether symmetry is obtained at 1st and 2nd order. To examine the 1st and 2nd order approximate Lie symmetries of the GMGHS black hole spacetime, 35 Lie symmetries (exact) of the Minkowski spacetime are used which forms an algebra sl(6, R). It is shown that no new approximate Lie symmetry exists at 1st and 2nd order and only exact 35 symmetries are recouped as trivial approximate Lie symmetries at both orders. Furthermore, no energy rescaling factor is seen in this spacetime. [ABSTRACT FROM AUTHOR]

In this paper, we prove that any group occurs as the group of homotopy classes of self-equivalences of a none elliptic Sullivan algebra. [ABSTRACT FROM AUTHOR]

Let M be a module over a commutative ring R. In this paper, we continue our study about the Zariski topology-graph G (τ T) which was introduced in Ansari-Toroghy et al. (Commun Algebra 42:3283–3296, 2014). For a non-empty subset T of Spec (M) , we obtain useful characterizations for those modules M for which G (τ T) is a bipartite graph. Also, we prove that if G (τ T) is a tree, then G (τ T) is a star graph. Moreover, we study coloring of Zariski topology-graphs and investigate the interplay between χ (G (τ T)) and ω (G (τ T)) . [ABSTRACT FROM AUTHOR]

In this paper, we prove that every rank one cubic derivation on a unital integral domain is identically zero. From this conclusion, under certain conditions, we achieve that the image of a cubic derivation on a commutative algebra is contained in the Jacobson radical of algebra. As the main result of the current study, we prove that every cubic derivation on a finite dimensional algebra, under some circumstances, is identically zero. [ABSTRACT FROM AUTHOR]

For a positive integer k ≥ 2, the kth-order slant weighted Toeplitz operator $${U_{k,\phi}^{\beta}}$$ on $${L^{2}(\beta)}$$ with $${\phi \in L^{\infty}(\beta)}$$ is defined as $${U_{k,\phi}^{\beta}=W_{k}M_{\phi}^{\beta}}$$ , where $${W_{k}e_{n}(z)=\frac{\beta_{m}}{\beta_{km}}e_m(z)}$$ if $${n=km, m\in\mathbb{Z}}$$ and $${W_{k}e_n(z)= 0}$$ if n ≠ km. The paper derives relations among the symbols of two kth-order slant weighted Toeplitz operators so that their product is a kth-order slant weighted Toeplitz operator. We also discuss the compactness and the case for two kth-order slant weighted Toeplitz operators to commute essentially. [ABSTRACT FROM AUTHOR]