Branching of symplectic groups is not multiplicity-free. We describe a new approach to resolving these multiplicities that is based on studying the associated branching algebra B. The algebra B is a graded algebra whose components encode the multiplicities of irreducible representations of Sp2n−2 in irreducible representations of Sp2n. Our rst theorem states that the map taking an element of Sp...

S OF PAPERS SUBMITTED FOR PRESENTATION TO THE SOCIETY The following papers have been submitted to the Secretary and the Associate Secretaries of the Society for presentation at meetings of the Society. They are numbered serially throughout this volume. Cross references to them in the reports of the meetings will give the number of this volume, the number of this issue, and the serial number of ...

In 2003, Di Nola, et.al. introduced the notion of MV -modules over a PMV algebra and A-ideals in MV -modules [5]. These are structures that naturally correspond to lu-modules over lu-rings [5]. Recall that an lu-ring is a pair (R,u), where (R, ⊕, ·, 0, ≤) is an l-ring and u is a strong unit of R (i.e, u is a strong unit of the underlying l-group) such that u · u ≤ u and l-ring is a structure (R...

An algebra homomorphism ψ from the q-deformed algebra U q (iso 2) with generating elements I, T 1 , T 2 and defining relations [I, T 2 ] q = T 1 , [T 1 , I] q = T 2 , [T 2 , T 1 ] q = 0 (where [A, B] q = q 1/2 AB − q −1/2 BA) to the extensionˆU q (m 2) of the Hopf algebra U q (m 2) is constructed. The algebra U q (iso 2) at q = 1 leads to the Lie algebra iso 2 ∼ m 2 of the group ISO(2) of motio...

Let V be a variety whose class of finite members has a decidable first-order theory. We prove that each finite member A of V satisfies the (3,1) and (3,2) transfer principles, and that the minimal sets of prime quotients of type 2 or 3 in A must have empty tails. The first result has already been used by J. Jeong [9] in characterizing the finite subdirectly irreducible members of V with nonabel...

Basic Logic was introduced by Petr Hájek to provide a uni ed approach to fuzzy logics, and judging by its rapid adoption in the research community, it has enjoyed considerable success in this regard. One of the reasons is that while it is a very general logic, it has elegant semantics with respect to the real unit interval, which allow for practical applications and use of standard software too...

A group is ^-separating if a Boolean power of the group has a unique Boolean algebra. It is proved that a finite subdirectly irreducible group is S-separating if and only if it is non-Abelian. Suppose B is a Boolean ring and G is a group. Let B[G] denote the group ring of G with coefficient ring B. The Boolean power G [B] is defined to be the set of those elements 2e,.g,. EB[G] such that (1) 2e...

We construct irreducible modules Vα, α ∈ C over W3 algebra with c = −2 in terms of a free bosonic field. We prove that these modules exhaust all the irreducible modules of W3 algebra with c = −2. Highest weights of modules Vα, α ∈ C with respect to the full (two-dimensional) Cartan subalgebra of W3 algebra are ( 1 2α(α − 1), 16α(α − 1)(2α − 1) ) . They are parametrized by points (t, w) on a rat...