121.
Algebras of quotients of Leavitt path algebras
- Molina, Mercedes Siles
We start this paper by showing that the Leavitt path algebra of a
(row-finite) graph is an algebra of quotients of the corresponding path
algebra. The path algebra is semiprime if and only if whenever there is a path
connecting two vertices, there is another one in the opposite direction.
Semiprimeness is studied because, for acyclic graphs, the Leavitt path algebra
is a Fountain-Gould algebra of right quotients of any semiprime subalgebra
containing the path algebra (and a Moore-Penrose algebra of right quotients of
any subalgebra with involution that contains the path algebra). The maximal
algebras of quotients of Leavitt path algebras with essential socle
(equivalently the associated graph...
122.
On boson algebras as Hopf algebras
- Tsohantjis, I; Paolucci, A; Jarvis, P D
Certain types of generalized undeformed and deformed boson algebras which
admit a Hopf algebra structure are introduced, together with their Fock-type
representations and their corresponding $R$-matrices. It is also shown that a
class of generalized Heisenberg algebras including those algebras including
those underlying physical models such as that of Calogero-Sutherland, is
isomorphic with one of the types of boson algebra proposed, and can be
formulated as a Hopf algebra.
123.
Non-associative algebras associated to Poisson algebras
- Goze, Michel; Remm, Elisabeth
Poisson algebras are usually defined as structures with two operations, a
commutative associative one and an anti-commutative one that satisfies the
Jacobi identity. These operations are tied up by a distributive law, the
Leibniz rule. We present Poisson algebras as algebras with one operation, which
enables us to study them as part of non-associative algebras. We study the
algebraic properties of Poisson algebras, give classifications in low dimension
and we define a cohomology to study their deformations as non-associative
algebras.
124.
Geometric algebra: a computational framework for geometrical applications (part I: algebra)
- Leo Dorst; Stephen Mann
Geometric algebra is a consistent computational framework in which to define geometric primitives and their relationships. This algebraic approach contains all geometric operators and permits specification of constructions in a coordinate-free manner. Thus, the ideas of geometric algebra are important for developers of CAD systems. This paper gives an introduction to the elements of geometric algebra, which contains primitives of any dimensionality (rather than just vectors), and an introduction to three of the products of geometric algebra, the geometric product, the inner product, and the outer product. These products are illustrated by using them to solve simple geometric problems.
125.
Geometric algebra: a computational framework for geometrical applications (part I: algebra)
- Leo Dorst; Stephen Mann
Geometric algebra is a consistent computational framework in which to define geometric primitives and their relationships. This algebraic approach contains all geometric operators and permits specification of constructions in a coordinate-free manner. Thus, the ideas of geometric algebra are important for developers of CAD systems. This paper gives an introduction to the elements of geometric algebra, which contains primitives of any dimensionality (rather than just vectors), and an introduction to three of the products of geometric algebra, the geometric product, the inner product, and the outer product. These products are illustrated by using them to solve simple geometric problems.
126.
Quasi-Hopf $*$-Algebras
- Gould, M. D.; Lekatsas, T.
We introduce quasi-Hopf $*$-algebras i.e. quasi-Hopf algebras equipped with a
conjugation (star) operation. The definition of quasi-Hopf $*$-algebras
proposed ensures that the class of quasi-Hopf $*$-algebras is closed under
twisting and additionally, that any Hopf $*$-algebra becomes a quasi-Hopf
$*$-algebra via twisting. The basic properties of these algebras are developed.
The relationship between the antipode and star structure is investigated.
Quasi-triangular quasi-Hopf $*$-algebras are introduced and studied.
127.
Simplicity of ultragraph algebras
- Tomforde, Mark
In this paper we analyze the structure of C*-algebras associated to
ultragraphs, which are generalizations of directed graphs. We characterize the
simple ultragraph algebras as well as deduce necessary and sufficient
conditions for an ultragraph algebra to be purely infinite and to be AF. Using
these techniques we also produce an example of an ultragraph algebra which is
neither a graph algebra nor an Exel-Laca algebra. We conclude by proving that
the C*-algebras of ultragraphs with no sinks are Cuntz-Pimsner algebras.
128.
Process algebra with nonstandard timing
- C. A. Middelburg
Abstract. The possibility of two or more actions to be performed consecutively at the same point in time is not excluded in the process algebras from the framework of process algebras with timing presented by Baeten and Middelburg [Handbook of Process Algebra, Elsevier, 2001, Chapter 10]. This possibility is useful in practice when describing and analyzing systems in which actions occur that are entirely independent. However, it is an abstraction of reality to assume that actions can be performed consecutively at the same point in time. In this paper, we propose a process algebra with timing in which this possibility...
129.
Hecke algebras of group extensions
- Baumgartner, Udo; Foster, James; Hicks, Jacqueline; Lindsay, Helen; Maloney, Ben; Raeburn, Iain; Ramagge, Jacqui; Richardson, Sarah
We describe the Hecke algebra ℋ(Γ,Γ₀) of a Hecke pair (Γ,Γ₀) in terms of the Hecke pair (N,Γ₀) where N is a normal subgroup of Γ containing Γ₀. To do this, we introduce twisted crossed products of unital *-algebras by semigroups. Then, provided a certain semigroup S ⊂ Γ/N satisfies S⁻¹ S = Γ/N, we show that ℋ(Γ,Γ₀) is the twisted crossed product of ℋ(N,Γ₀) by S . This generalizes a recent theorem of Laca and Larsen about Hecke algebras of semidirect products.
130.
Hecke algebras of group extensions
- Baumgartner, Udo; Foster, James; Hicks, Jacqueline; Lindsay, Helen; Maloney, Ben; Raeburn, Iain; Ramagge, Jacqui; Richardson, Sarah
We describe the Hecke algebra ℋ(Γ,Γ₀) of a Hecke pair (Γ,Γ₀) in terms of the Hecke pair (N,Γ₀) where N is a normal subgroup of Γ containing Γ₀. To do this, we introduce twisted crossed products of unital *-algebras by semigroups. Then, provided a certain semigroup S ⊂ Γ/N satisfies S⁻¹ S = Γ/N, we show that ℋ(Γ,Γ₀) is the twisted crossed product of ℋ(N,Γ₀) by S . This generalizes a recent theorem of Laca and Larsen about Hecke algebras of semidirect products.
131.
Q-multilinear Algebra
- Isaev, A.; Ogievetsky, O.; Pyatov, P.
The Cayley-Hamilton-Newton theorem - which underlies the Newton identities
and the Cayley-Hamilton identity - is reviewed, first, for the classical
matrices with commuting entries, second, for two q-matrix algebras, the
RTT-algebra and the RLRL-algebra. The Cayley-Hamilton-Newton identities for
these q-algebras are related by the factorization map. A class of algebras
M(R,F) is presented. The algebras M(R,F) include the RTT-algebra and the
RLRL-algebra as particular cases. The algebra M(R,F) is defined by a pair of
compatible matrices R and F. The Cayley-Hamilton-Newton theorem for the
algebras M(R,F) is stated. A nontrivial example of a compatible pair is given.
132.
Quantum W-algebras and Elliptic Algebras
- Feigin, Boris; Frenkel, Edward
We define quantum W-algebras generalizing the results of Reshetikhin and the
second author, and Shiraishi-Kubo-Awata-Odake. The quantum W-algebra associated
to sl_N is an associative algebra depending on two parameters. For special
values of parameters it becomes the ordinary W-algebra of sl_N, or the
q-deformed classical W-algebra of sl_N. We construct free field realizations of
the quantum W-algebras and the screening currents. We also point out some
interesting elliptic structures arising in these algebras. In particular, we
show that the screening currents satisfy elliptic analogues of the Drinfeld
relations in U_q(n^).
133.
Teorema de Ramsey aplicado a álgebras de Boole
- Benítez Trujillo, Francisco
Some properties of Boolean algebras are characterized through the topological properties of a certain space of countable sequences of ordinals. For this, it is necessary to prove the Ramsey theorems for an arbitrary infinite cardinal. Also, we define continuous mappings on these spaces from vector measures on the algebra.
134.
How Iterative are Iterative Algebras?
- Stefan Milius
Iterative algebras are defined by the property that every guarded system of recursive equations has a unique solution. We prove that they have a much stronger property: every system of recursive equations has a unique strict solution. And we characterize those systems that have a unique solution in every iterative algebra.
135.
Smooth *-algebras
- Dubois-Violette, Michel; Kriegl, Andreas; Maeda, Yoshiaki; Michor, Peter W.
Looking for the universal covering of the smooth non-commutative torus leads
to a curve of associative multiplications on the space $\Cal O_M'(\Bbb
R^{2n})\cong \Cal O_C(\Bbb R^{2n})$ of Laurent Schwartz which is smooth in the
deformation parameter $\hbar$. The Taylor expansion in $\hbar$ leads to the
formal Moyal star product. The non-commutative torus and this version of the
Heisenberg plane are examples of smooth *-algebras: smooth in the sense of
having many derivations. A tentative definition of this concept is given.
136.
Cyclotomic Nazarov-Wenzl algebras
- Ariki, Susumu; Mathas, Andrew; Rui, Hebing
Nazarov \cite{Nazarov:brauer} introduced an infinite dimensional algebra,
which he called the \textit{affine Wenzl algebra}, in his study of the Brauer
algebras. In this paper we study certain ``cyclotomic quotients'' of these
algebras. We construct the irreducible representations of these algebras in the
generic case and use this to show that these algebras are free of rank
$r^n(2n-1)!!$ (when $\Omega$ is $\bu$--admissible). We next show that these
algebras are cellular and give a labelling for the simple modules of the
cyclotomic Nazarov--Wenzl algebras over an arbitrary field. In particular, this
gives a construction of all of the finite dimensional irreducible modules of
the affine Weyl algebra (when $\Omega$ is admissible).
137.
Homomorphisms on some function algebras
- Jaramillo Aguado, Jesús Angel; Gómez Gil, J.; Garrido, M. I.
Suppose that A is an algebra of continuous real functions defined on a topological space X. We shall be concerned here with the problem as to whether every nonzero algebra homomorphism f: A ? R is given by evaluation at some point of X, in the sense that there exists some a in X such that f(f) = f(a) for every f in A. The problem goes back to the work of Michael [19], motivated by the question of automatic continuity of homomorphisms in a symmetric *-algebra. More recently, the problem has been considered by several authors, mainly in the...
138.
Completions of Cellular Algebras
- Green, R. M.
We introduce procellular algebras, so called because they are inverse limits
of finite dimensional cellular algebras as defined by Graham and Lehrer. A
procellular algebra is defined as a certain completion of an infinite
dimensional cellular algebra whose cell datum is of ``profinite type''. We show
how these notions overcome some known obstructions to the theory of cellular
algebras in infinite dimensions.
139.
Symmetric quantum Weyl algebras
- Diaz, Rafael; Pariguan, Eddy
We study the symmetric powers of four algebras: $q$-oscillator algebra,
$q$-Weyl algebra, $h$-Weyl algebra and $U({\mathfrak {sl}}_2)$. We provide
explicit formulae as well as combinatorial interpretation for the normal
coordinates of products of arbitrary elements in the above algebras.
140.
Inhomogeneous Yang-Mills algebras
- Berger, Roland; Dubois-Violette, Michel
We determine all inhomogeneous Yang-Mills algebras and super Yang-Mills
algebras which are Koszul. Following a recent proposal, a non-homogeneous
algebra is said to be Koszul if the homogeneous part is Koszul and if the PBW
property holds. In this paper, the homogeneous parts are the Yang-Mills algebra
and the super Yang-Mills algebra.
