One-sided division absolute valued algebras.

Rodríguez Palacios, Ana. "One-sided division absolute valued algebras.." Publicacions Matemàtiques 36.2B (1992): 925-954. <http://eudml.org/doc/41761>.

@article{RodríguezPalacios1992,
abstract = {We develop a structure theory for left divsion absolute valued algebras which shows, among other things, that the norm of such an algebra comes from an inner product. Moreover, we prove the existence of left division complete absolute valued algebras with left unit of arbitrary infinite hilbertian division and with the additional property that they have nonzero proper closed left ideals. Our construction involves results from the representation theory of the so called "Canonical Anticommutation Relations" in Quantum Mechanics. We also show that homomorphisms from complete normed algebras into arbitrary absolute valued algebras are contractive, hence automatically continuous.},
author = {Rodríguez Palacios, Ana},
journal = {Publicacions Matemàtiques},
keywords = {canonical anticommutation relations; structure theory for left division absolute valued algebras; inner product; representation theory; homomorphisms from complete normed algebras into arbitrary absolute valued algebras are contractive},
language = {eng},
number = {2B},
pages = {925-954},
title = {One-sided division absolute valued algebras.},
url = {http://eudml.org/doc/41761},
volume = {36},
year = {1992},
}

TY - JOUR
AU - Rodríguez Palacios, Ana
TI - One-sided division absolute valued algebras.
JO - Publicacions Matemàtiques
PY - 1992
VL - 36
IS - 2B
SP - 925
EP - 954
AB - We develop a structure theory for left divsion absolute valued algebras which shows, among other things, that the norm of such an algebra comes from an inner product. Moreover, we prove the existence of left division complete absolute valued algebras with left unit of arbitrary infinite hilbertian division and with the additional property that they have nonzero proper closed left ideals. Our construction involves results from the representation theory of the so called "Canonical Anticommutation Relations" in Quantum Mechanics. We also show that homomorphisms from complete normed algebras into arbitrary absolute valued algebras are contractive, hence automatically continuous.
LA - eng
KW - canonical anticommutation relations; structure theory for left division absolute valued algebras; inner product; representation theory; homomorphisms from complete normed algebras into arbitrary absolute valued algebras are contractive
UR - http://eudml.org/doc/41761
ER -