We consider maps of the family of convex bodies in Euclidean ddimensional space into itself that are compatible with certain structures on this family: A Minkowski-endomorphism is a continuous, Minkowski-additive map that commutes with rotations. For d ≥ 3, a representation theorem for such maps is given, showing that they are mixtures of certain prototypes. These prototypes are obtained by app...

In this paper we investigate the conditions under which a given ring is a sub-ring of a semi-simple ring. For convenience, we say that a ring A is an extension of a ring B, if B is a sub-ring of A. It is found that the existence of a semi-simple extension is equivalent to the vanishing of the extension radical, a two-sided ideal defined analogously to the ordinary radical. In Theorem II we give...

We study relations between the quadraticity of Kuranishi family a coherent sheaf on complex projective scheme and formality DG-Lie algebra its derived endomorphisms. In particular, we prove that for polystable smooth surface endomorphisms is formal if only quadratic.

We extend the notion of ‘homomorphism-homogeneity’ to a wider class of kinds of maps than previously studied, and we investigate the relations between the resulting notions of homomorphism-homogeneity, giving several examples. We also give further details on related work reported in [Deborah Lockett and John K. Truss, Generic endomorphisms of homogeneous Structures,in ‘Groups and model theory’,...

Abstract. We present a systematic way to generate critically finite endomorphisms of Pn. These maps arise in the context of Teichmüller theory, specifically in Thurston’s topological characterization of rational maps. The dynamical objects for the endomorphisms correspond to central objects from Thurston’s theorem. Our theorems build infinitely many of these endomorphisms; in fact, a large numb...

In the framework of locally covariant quantum field theory, a theory is described as a functor from a category of spacetimes to a category of ∗-algebras. It is proposed that the global gauge group of such a theory can be identified as the group of automorphisms of the defining functor. Consequently, multiplets of fields may be identified at the functorial level. It is shown that locally covaria...

For a compact space X we consider extending endomorphisms of the algebra C(X) to be endomorphisms of Arens-Hoffman and Cole extensions of C(X). Given a non-linear, monic polynomial p ∈ C(X)[t], with C(X)[t]/pC(X)[t] semi-simple, we show that if an endomorphism of C(X) extends to the Arens-Hoffman extension with respect to p then it also extends to the simple Cole extension with respect to p. We...

The inner automorphisms of a group G can be characterized within the category of groups without reference to group elements: they are precisely those automorphisms of G that can be extended, in a functorial manner, to all groups H given with homomorphisms G→ H. (Precise statement in §1.) The group of such extended systems of automorphisms, unlike the group of inner automorphisms of G itself, is...

For $p\geq 2$, the $p$-adic ring $C^*$-algebra $\mathcal {Q}_p$ is universal generated by a unitary $U$ and an isometry $S_p$ such that $S_pU=U^pS_p$ $\sum _{l=0}^{p-1}U^lS_pS_p^*U^{-l}=1$. any $k$ coprime to $p$ we define end

H. Weyl has defined a semi-simple algebra (of finite rank) to be an algebra which admits a faithful semi-simple linear representation. Now, algebras are rings with a field of operators; Artin and others have shown that the theory of semi-simple algebras can be generalized to a theory of semi-simple rings (without the field of operators) provided we replace the condition of finite rank by suitab...