This paper examines actions of right LCM semigroups by endomorphisms C*-algebras that encode an additional structure the semigroup. We define contractive covariant representations for these semigroup dynamical systems and prove a generalized Stinespring's dilation theorem showing can be dilated if only map on C*-algebra is unital completely positive. generalizes earlier results about dilations ...

We give a formula for the Betti numbers of 3-Sasakian manifolds or orbifolds which can be obtained as 3-Sasakian quotients of a sphere by a torus. This answers a question of Galicki and Salamon about the topology of 3-Sasakian manifolds. A (4m+3)-dimensional manifold is 3-Sasakian if it possesses a Riemannian metric with three orthonormal Killing elds deening a local SU(2)-action and satisfying...

We study algebraic and topological properties of topological semigroups containing a copy of the bicyclic semigroup C(p, q). We prove that each topological semigroup S with pseudocompact square contains no dense copy of C(p, q). On the other hand, we construct a consistent example of a Tychonov countably compact semigroup containing a copy of C(p, q). In this paper we study the structural prope...

A semigroup S is said to have the compactness property, or CP for short, if each system of equations over a nite set of variables has an equivalent nite subsystem, that is, having exactly the same solutions in S. We prove that a completely 0-simple semigroup S satis es CP if and only if the group G in a Rees matrix representation S = M0(I; G; ;P) satis es this property. Further, a variety of co...

Using a variant of Schreier’s Theorem, and the theory of Green’s relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to which these results apply include many important classes: transformation semigroups, partial permutation semigroups and inverse semigroups, partition monoids...

Notation 1.1. Let X be a projective variety over an algebraically closed field. For every integer k ≥ 0, denote by Nk(X) the finitely-generated free Abelian group of k-cycles modulo numerical equivalence, and denote by N(X) the k graded piece of the quotient algebra A∗(X)/Num∗(X), cf. [Ful98, Example 19.3.9]. For every Z-module B, denote Nk(X)B := Nk(X)⊗B, resp. N(X)B := N(X)⊗B. Denote by NEk(X...

A right ideal (left ideal, two-sided ideal) is a non-empty language L over an alphabet Σ such that L = LΣ∗ (L = Σ∗L, L = Σ∗LΣ∗). Let k = 3 for right ideals, 4 for left ideals and 5 for two-sided ideals. We show that there exist sequences (Ln | n > k) of right, left, and two-sided regular ideals, where Ln has quotient complexity (state complexity) n, such that Ln is most complex in its class und...

Introduction Let B = k[x 1 ,. .. , x n ] be a polynomial ring over a field k and A = B/J a quotient ring of B by a homogeneous ideal J. Let m denote the maximal graded ideal of A. Then the Rees algebra R = A[mt] may be considered a standard graded k-algebra and has a presentation B[y 1 ,. In this paper we want to compare the ideals J and I J as well as their homological properties.