32 research outputs found
Albert algebras over Z and other rings
Albert algebras, a specific kind of Jordan algebra, are naturally
distinguished objects among commutative non-associative algebras and also arise
naturally in the context of simple affine group schemes of type , ,
or . We study these objects over an arbitrary base ring , with
particular attention to the case of the integers. We prove in this generality
results previously in the literature in the special case where is a field
of characteristic different from 2 and 3.Comment: v2: section 12 on number of generators is new, Theorem 13.5 now holds
for semi-local rings (and even a somewhat wider class
Wild Pfister forms over Henselian fields, K-theory, and conic division algebras
The epicenter of this paper concerns Pfister quadratic forms over a field
with a Henselian discrete valuation. All characteristics are considered but we
focus on the most complicated case where the residue field has characteristic 2
but does not. We also prove results about round quadratic forms,
composition algebras, generalizations of composition algebras we call conic
algebras, and central simple associative symbol algebras. Finally we give
relationships between these objects and Kato's filtration on the Milnor
-groups of
Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum
A quantum version of transition state theory based on a quantum normal form
(QNF) expansion about a saddle-centre-...-centre equilibrium point is
presented. A general algorithm is provided which allows one to explictly
compute QNF to any desired order. This leads to an efficient procedure to
compute quantum reaction rates and the associated Gamov-Siegert resonances. In
the classical limit the QNF reduces to the classical normal form which leads to
the recently developed phase space realisation of Wigner's transition state
theory. It is shown that the phase space structures that govern the classical
reaction d ynamicsform a skeleton for the quantum scattering and resonance
wavefunctions which can also be computed from the QNF. Several examples are
worked out explicitly to illustrate the efficiency of the procedure presented.Comment: 132 pages, 31 figures, corrected version, Nonlinearity, 21 (2008)
R1-R11