In this paper we construct “structural” pre-braidings characterizing different algebraic structures: a rack, an associative algebra, a Leibniz algebra and their representations. Some of these pre-braidings seem original. On the other hand, we propose a general homology theory for pre-braided vector spaces and braided modules, based on the quantum co-shuffle comultiplication. Applied to the stru...

We consider the GNS Hilbert space H of a uniformly hyper-finite C∗algebra and study a class of unbounded Lindbladian arises from commutators. Exploring the local structure of UHF algebra, we have shown that the associated Hudson-Parthasarathy type quantum stochastic differential equation admits a unitary solution. The vacuum expectation of homomorphic cocycle, implemented by the Hudson-Parthasa...

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

Abstract Hyper-Kamiokande (Hyper-K) is a next generation underground large water Cherenkov detector. Its tank will be filled with 260000 metric tons of ultra-pure fiducial volume 0.19 Mtons, which about 8 times larger than that its predecessor Super-Kamiokande. In volume, light produced by neutrino interactions and detected newly developed photo sensors installed in dedicated frame. Two differe...

In this paper, by using Gröbner-Shirshov bases, we show that in the following classes, each (resp. countably generated) algebra can be embedded into a simple (resp. two-generated) algebra: associative differential algebras, associative Ω-algebras, associative λ-differential algebras. We show that in the following classes, each countably generated algebra over a countable field k can be embedded...

Let A+(k) denote the ring l~[ t] / t k+t and let fr be a reductive complex Lie algebra with exponents m 1 . . . . . m,. This paper concerns the Lie algebra cohomology of ~| considered as a bigraded algebra (here one of the gradings is homological degree and the other, which we call weight, is inherited from the obvious grading of f f | § (k)). We conjecture that this Lie algebra cohomology is a...

We prove that for a von Neumann algebra that is an algebraic K system with respect to some automorphism, the invariant state is K{clustering and r{clustering. Further we study in examples how far the von Neumann algebra inherits the K property from the underlying C algebra.

In commutative algebra, a Weitzenböck derivation is a nonzero triangular linear derivation of the polynomial algebra K[x1, . . . , xm] in several variables over a field K of characteristic 0. The classical theorem of Weitzenböck states that the algebra of constants is finitely generated. (This algebra coincides with the algebra of invariants of a single unipotent transformation.) In this paper ...

Let K be a finite abelian extension of the rational field Q. If A is a central simple algebra over K then we let [A] denote the class of A in the Brauer group B(K) of K. The Schur subgrozcp S(K) of B{K) consists of those algebra classes which contain a simple component of the group algebra K[GJ for some finite group G. M. Benard and M. Schacher [2, Theorem 1, p. 3801 have shown that if [A] is i...