منابع مشابه
un 2 00 0 On representations of partial ∗ - algebras based on B - weights
A generalization of the GNS-representation is investigated that represents partial ∗-algebras as systems of operators acting on a partial inner product space (PIP -space). It is based on possibly indefinite B-weights which are closely related to the positive B-weights introduced by J.-P. Antoine, Y. Soulet and C. Trapani. Some additional assumptions had to be made in order to guarantee the GNS-...
متن کاملSerre Weights for Quaternion Algebras
We study the possible weights of an irreducible 2-dimensional mod p representation of Gal(F/F ) which is modular in the sense of that it comes from an automorphic form on a definite quaternion algebra with centre F which is ramified at all places dividing p, where F is a totally real field. In most cases we determine the precise list of possible weights; in the remaining cases we determine the ...
متن کاملLie Algebras: Abstract Theory of Weights
Proof. I will check the four axioms of the root system. (R1) Since |Φ∨| = |Φ|, then Φ∨ is finite. Since Φ spans E and α∨ is a non-zero scalar multiple of α for all α ∈ Φ, then Φ∨ spans E and 0 / ∈ Φ∨. (R2) Since (−α)∨ = 2(−α) ((−α),(−α)) = − 2α (α,α) = −α∨, then the only multiples of α∨ are ±α∨. (R3) I need to show that if α∨ ∈ Φ∨ then the reflection σα∨ leaves Φ∨ invariant. Let α in Φ, then fo...
متن کاملOn Surjective Kernels of Partial Algebras
A partial algebra A = (A, F ) is called surjective if each of its elements lies in the range of some of its operations. By a transfinite iteration construction over the class of all ordinals it is proved that in each partial algebra A there exists the largest surjective subalgebra Skr A, called the surjective kernel of A. However, what might be found a bit surprising, for each ordinal α there i...
متن کاملOn Completability of Partial Combinatory Algebras
A Partial Combinatory Algebra is completable if it can be extended to a total one. Klop [11, 12] gave a sufficient condition for completability of a PCA M = (M, ·,K, S) in the form of ten axioms (inequalities) on terms of M . We prove that Klop’s sufficient condition is equivalent to the existence of an injective s-m-n function over M (that in turns is equivalent to the Padding Lemma). This is ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1995
ISSN: 0022-247X
DOI: 10.1006/jmaa.1995.1212