The Iwasawa algebra is a power series ring in one variable over the -adic integers. It has long been studied by number theorists in the context of -extensions of number fields. It also arises, however, as a ring of operations in -adic topological -theory. In this paper we study -local stable homotopy theory using the structure theory of modules over the Iwasawa algebra. In particular, for odd we classify -local spectra up to pseudo-equivalence (the analogue of pseudo-isomorphism for -modules) and give an Iwasawa-theoretic classification of the thick subcategories of the weakly dualizable spectra.
In the first section of this paper we revisit the definition and some of the properties of the minimal polynomial of an element of a finite-dimensional power-associative algebra over an arbitrary field . Our main observation is that , the minimal polynomial of , may depend not only on , but also on the underlying algebra. More precisely, if is a subalgebra of , and if is the minimal polynomial of in , then may differ from , in which case we have .
In the second section we restrict attention to the case where is either the real or the complex numbers, and define , the radius of an element in , to be the largest root in absolute value of the minimal polynomial of . We show that possesses some of the familiar properties of the classical spectral radius. In particular, we prove that is a continuous function on .
In the third and last section, we deal with stability of subnorms acting on subsets of finite-dimensional power-associative algebras. Following a brief survey, we enhance our understanding of the subject with the help of our findings of the previous section. Our main new result states that if , a subset of an algebra , satisfies certain assumptions, and is a continuous subnorm on , then is stable on if and only if majorizes the radius defined above.
For each piecewise monotonic map of , we associate a pair of C*-algebras and and calculate their K-groups. The algebra is an AI-algebra. We characterize when and are simple. In those cases, has a unique trace, and is purely infinite with a unique KMS state. In the case that is Markov, these algebras include the Cuntz-Krieger algebras , and the associated AF-algebras . Other examples for which the K-groups are computed include tent maps, quadratic maps, multimodal maps, interval exchange maps, and -transformations. For the case of interval exchange maps and of -transformations, the C*-algebra coincides with the algebras defined by Putnam and Katayama-Matsumoto-Watatani, respectively.
Let G be an abelian group, ε an anti-bicharacter of G and L a G-graded ε Lie algebra (color Lie algebra) over a field of characteristic zero. We prove that for all G-graded, positively filtered A such that the associated graded algebra is isomorphic to the G-graded ε-symmetric algebra S(L), there is a G- graded ε-Lie algebra L and a G-graded scalar two cocycle , such that A is isomorphic to Uω(L) the generalized enveloping algebra of L associated with ω. We also prove there is an isomorphism of graded spaces between the Hochschild cohomology of the generalized universal enveloping
algebra U(L) and the generalized cohomology of the color Lie algebra L.
Supported by the EC project Liegrits MCRTN 505078. 相似文献
We investigate a theory in which fundamental objects are branes described in terms of higher grade coordinates encoding both the motion of a brane as a whole, and its volume evolution. We thus formulate a dynamics which generalizes
the dynamics of the usual branes. Geometrically, coordinates and associated coordinate frame fields {} extend the notion of geometry from spacetime to that of an enlarged space, called Clifford space or C-space. If we start
from four-dimensional spacetime, then the dimension of C-space is 16. The fact that C-space has more than four dimensions
suggests that it could serve as a realization of Kaluza-Klein idea. The “extra dimensions” are not just the ordinary extra
dimensions, they are related to the volume degrees of freedom, therefore they are physical, and need not be compactified.
Gauge fields are due to the metric of Clifford space. It turns out that amongst the latter gauge fields there also exist higher
grade, antisymmetric fields of the Kalb–Ramond type, and their non-Abelian generalization. All those fields are naturally
coupled to the generalized branes, whose dynamics is given by a generalized Howe–Tucker action in curved C-space. 相似文献
We have established a new method of aberration analysis for off-axial optical systems which are generalized concepts of co-axial optical systems, by introducing two kinds of newly defined 4-element vectors and expanding these vectors with the help of tensor algebra. In this method, since aberration properties are represented in tensor form, we can easily formulate the aberration relations between different azimuths. We can then evaluate the azimuth dependence of aberration properties in greater detail by separating them into inherent optical properties parts, which are independent of azimuths, and the paraxial ray-tracing part, which includes the expression of the evaluation azimuth. 相似文献
An algebraic approach for extending Hamiltonian operators is proposed. A relevant sufficient condition for generating new Lie algebras from known ones is presented. Some special cases are discussed and several illustrative examples are given. 相似文献