Extreme positive operators and homomorphisms

Clifford Homomorphisms and Higher Spin Dirac Operators

We present a generalization of the Clifford action for other representations spaces of Spin(n), which is called the Clifford homomorphism. Their properties extend to the ones for the higher spin Dirac operators on spin manifolds. In particular, we have general Bochner identities for them, and an eigenvalue estimate of a Laplace type operator on any associated bundle.

Gödel Homomorphisms as Gödel Modal Operators

We extend propositional Gödel logic by a unary modal operator, which we interpret as 5 Gödel homomorphisms, i.e. functions [0, 1] → [0, 1] that distribute over the interpretations of the 6 binary connectives of Gödel logic. We show that validity in the propositional fragment has a simple 7 superintuitionistic Hilbert-type proof system, which is not structurally complete, and that validity 8 doe...

On Extreme Averaging Operators

Sub-principal Homomorphisms in Positive Characteristic

LetG be a reductive group over an algebraically closed field of characteristic p, and let u ∈ G be a unipotent element of order p. Suppose that p is a good prime for G. We show in this paper that there is a homomorphism φ : SL2/k → G whose image contains u. This result was first obtained by D. Testerman (J. Algebra, 1995) using case considerations for each type of simple group (and using, in so...

Homomorphisms of local algebras in positive characteristic

Article history: Received 19 December 2008 Available online xxxx Communicated by Steven Dale Cutkosky Dedicated to Professor Shuzo Izumi