Hopf representation is a module and comodule with a consistency condition that is more general than the consistency condition of Hopf modules. For a Hopf algebra H, we construct an induced Hopf representation from a representation of a bialgebra B using a bialgebra epimorphism π : H → B. Application on the quantum group Eq(2) is given. Mathematics Subject Classification: 16T05, 06B15, 17B37

Suppose A is a C*-algebra and B is a Banach algebra such that it can be continuously imbedded in B(H), the Banach algebra of bounded linear operators on some Hubert space H. It is shown that if 6 is a compact algebra homomorphism from A into B, then 6 is a finite rank operator, and the range of 0 is spanned by a finite number of idempotents. If, moreover, B is commutative, then 9 has the form 8...

We show that a deformation of the Heisenberg algebra which depends on a dimensionful parameter κ is the algebraic structure which underlies the generalized uncertainty principle in quantum gravity. The deformed algebra and therefore the form of the generalized uncertainty principle are fixed uniquely by rather simple assumptions. The string theory result is reproduced expanding our result at fi...

Variant satisfiability is a theory-generic algorithm to decide quantifier-free satisfiability in an initial algebra TΣ{E when the theory pΣ,Eq has the finite variant property and its constructors satisfy a compactness condition. This paper: (i) gives a precise definition of several meta-level sub-algorithms needed for variant satisfiability; (ii) proves them correct; and (iii) presents a reflec...

(2+2)–dimensional quantum mechanical q–phase space which is the semi– direct product of the quantum planeEq(2)/U(1) and its dual algebra eq(2)/u(1) is constructed. Commutation and the resulting uncertainty relations are studied. ”Quantum mechanical q–Hamiltonian” of the motion over the quantum plane is derived and the solution of the Schrödinger equation for the q– semiclassical motion governed...

Let ~ be a property which can be attributed to 0, 1-sublattices of Eq (X), X arbitrary. (Eq (X) is the lattice of all equivalence relations on X.) For example, could be modularity or permutability. It was proved in [3] that for every integer k 2 there is an n -> 1 such that for every algebra A of cardinality k, if Con (A m) satisfies ~ for all m -< n then Con (A m) satisfies ~ for all m. Let ne...

In these notes I discuss Monte Carlo simulations for the study of classical models in statistical mechanics. I include a simple and direct proof that the method converges to the Boltzmann distribution. Usually, physics articles discuss this important point by just giving a reference to the mathematical literature on " Markov chains " , where the proof is rather abstract. In these notes I give a...

This theory defines a type constructor representing the free Boolean algebra over a set of generators. Values of type (α)formula represent propositional formulas with uninterpreted variables from type α, ordered by implication. In addition to all the standard Boolean algebra operations, the library also provides a function for building homomorphisms to any other Boolean algebra type. 1 Free Boo...

A well-known result of universal algebra states: every algebraic lattice is isomorphic to the congruence lattice of an algebra. It is natural to ask whether every finite lattice occurs as the congruence lattice of a finite algebra. This fundamental question, asked over 45 years ago, is among the most elusive problems of universal algebra. Call a finite lattice L “representable” if it is the con...

Poultry industry is an important production system due to providing remarkable portion of the human food and protein needs. Considering the necessity of environmental protection, the amount of environmental impacts of a turkey production unit in Iran was determined using life cycle assessment method. The required information were collected through questionnaires and interviews with farm owners....