An adaption of Rieeel's notion of`strict deformation quantization' is applied to a particle moving on an arbitrary Riemannian manifold Q in an external gauge eld, that is, a connection on a principal H-bundle P over Q. Hence the Poisson algebra A 0 = C 0 ((T P)=H) is deformed into the C-algebra A = K(L 2 (P)) H of H-invariant compact operators on L 2 (P), which is isomorphic to K(L 2 (Q)) C (H)...

We prove the existence of a strict deformation quantization for the canonical Poisson structure on the dual of an integrable Lie algebroid. It follows that any Lie groupoid C-algebra may be regarded as a result of a quantization procedure. The C-algebra of the tangent groupoid of a given Lie groupoid G (with Lie algebra G) is the C-algebra of a continuous field of C-algebras over R with fibers ...

A minimum depth is assigned to a ring homomorphism and a bimodule over its codomain. When the homomorphism is an inclusion and the bimodule is the codomain, the recent notion of depth of a subring in a paper by Boltje-Danz-Külshammer is recovered . Subring depth below an ideal gives a lower bound for BDK’s subring depth of a group algebra pair or a semisimple complex algebra pair.

Let $nin mathbb{N}$. An additive map $h:Ato B$ between algebras $A$ and $B$ is called $n$-Jordan homomorphism if $h(a^n)=(h(a))^n$ for all $ain A$. We show that every $n$-Jordan homomorphism between commutative Banach algebras is a $n$-ring homomorphism when $n < 8$. For these cases, every involutive $n$-Jordan homomorphism between commutative C-algebras is norm continuous.

We give conditions for the exactness of Rokhlin skew products, apply these to random walks on locally compact, second countable topological groups and obtain that the Poisson boundary of a globally supported random walk on such a group is weakly mixing. S is a measurable homomorphism). We give (theorem 2.3) conditions for the exactness of the Rokhlin endomorphism T = These conditions are applie...

A classical theorem of Burnside asserts that if X is a faithful complex character for the finite group G, then every irreducible character of G is a constituent of some power Xn of X . Fifty years after this appeared, Steinberg generalized it to a result on semigroup algebras K[G] with K an arbitrary field and with G a semigroup, finite or infinite. Five years later, Rieffel showed that the the...

In this paper we prove the Schur-Weyl duality between the symplectic group and the Brauer algebra over an arbitrary infinite field K. We show that the natural homomorphism from the Brauer algebra Bn(−2m) to the endomorphism algebra of the tensor space (K2m)⊗n as a module over the symplectic similitude group GSp2m(K) (or equivalently, as a module over the symplectic group Sp2m(K)) is always surj...

In this note we consider an arbitrary submanifold C of a Poisson manifold P and ask whether it can be embedded coisotropically in some bigger submanifold of P . We define the classes of submanifolds relevant to the question (coisotropic, Poisson-Dirac, pre-Poisson ones), present an answer to the above question and consider the corresponding picture at the level of Lie groupoids, making concrete...

We exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial algebra R = C[X1, . . . , Xn] endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the semiclassical limit of the dualising bimodule for Hochschild homology of the corresponding quantum affine space. As a coro...

Non-commutative Poisson algebras are the algebras having an associative algebra structure and a Lie structure together with the Leibniz law. The non-commutative Poisson algebra structures on the infinite-dimensional algebras are studied. We show that these structures are standard on the poset subalgebras of the associative algebra of all endomorphisms of the countable-dimensional vector space T...