Silting and Tilting for Weakly Symmetric Algebras

If A is a finite-dimensional symmetric algebra, then it is well-known that the only silting complexes in Kb(projA) are the tilting complexes. In this note we investigate to what extent the same can be said for weakly symmetric algebras. On one hand, we show that this holds for all tilting-discrete weakly symmetric algebras. In particular, a tilting-discrete weakly symmetric algebra is also silting-discrete. On the other hand, we also construct an example of a weakly symmetric algebra with silting complexes that are not tilting.

Identifying the Positive Definiteness of Even-Order Weakly Symmetric Tensors via Z-Eigenvalue Inclusion Sets

The positive definiteness of even-order weakly symmetric tensors plays important roles in asymptotic stability of time-invariant polynomial systems. In this paper, we establish two Brauer-type Z-eigenvalue inclusion sets with parameters by Z-identity tensors, and show that these inclusion sets are sharper than existing results. Based on the new Z-eigenvalue inclusion sets, we propose some sufficient conditions for testing the positive definiteness of even-order weakly symmetric tensors, as well as the asymptotic stability of time-invariant polynomial systems. The given numerical experiments are reported to show the efficiency of our results.

On generalized weakly symmetric Kenmotsu manifolds

This paper aims to introduce the notions of a generalized weakly symmetric Kenmotsu manifolds and a generalized weakly Ricci-symmetric Kenmotsu manifolds. The existence of a generalized weakly symmetric Kenmotsu manifold is ensured by a non-trivial example.