scholarly journals Classification of Quantum Tori with Involution

2002 ◽  
Vol 45 (4) ◽  
pp. 711-731 ◽  
Author(s):  
Yoji Yoshii
Keyword(s):  
Lie Algebras ◽  
Root Systems ◽  
Type A ◽  
Affine Lie Algebras ◽  
Precise Information ◽  
Quantum Tori ◽  
Type C

AbstractQuantum tori with graded involution appear as coordinate algebras of extended affine Lie algebras of type A1, C and BC. We classify them in the category of algebras with involution. From this, we obtain precise information on the root systems of extended affine Lie algebras of type C.

MRI analysis and surgical treatment of Wassel Type IV duplicated thumbs

2021 ◽  
pp. 175319342098321
Author(s):  
Anyuan Wang ◽  
Jian Ding ◽  
Long Wang ◽  
Tinggang Chu ◽  
Zhipeng Wu ◽  
...  
Keyword(s):  
Type A ◽  
Surgical Reconstruction ◽  
Mri Findings ◽  
Level Of Evidence ◽  
Type D ◽  
Type Iv ◽  
Secondary Operations ◽  
Type C

We present the MRI findings for 39 Wassel Type IV duplicated thumbs in 38 patients. We found that MRI revealed the morphology of the cartilaginous connection between the thumb anlages and the location of the deviation corresponding to the classification of Horii, which allowed precise preoperative planning of corrective osteotomies. All 39 thumbs were available for follow-up after surgical reconstruction at a mean of 29 months (range 25 to 39). Four out of nine Horii Type A cases and all 12 Type B, as well as the six Type C and the six Type D cases, achieved good results according to the Tada scoring system. Five Type A cases achieved fair results with residual stiffness of the interphalangeal joint. No secondary operations were needed. We conclude that MRI proved useful in subclassifying Wassel Type IV duplicated thumbs and may aid in planning the osteotomies needed for their reconstruction. Level of evidence: IV

A New Classification of Cochleovestibular Malformations and Implications for Predicting Speech Perception Ability after Cochlear Implantation

2015 ◽  
Vol 20 (2) ◽  
pp. 90-101 ◽  
Author(s):  
Sung-Wook Jeong ◽  
Lee-Suk Kim
Keyword(s):  
Speech Perception ◽  
Cochlear Implantation ◽  
Test Scores ◽  
Type A ◽  
Cochlear Nerve ◽  
Type B ◽  
New Classification ◽  
Type D ◽  
Type C

Objectives: The aims of this study were to introduce a new classification of cochleovestibular malformation (CVM) and to investigate how well this classification can predict speech perception ability after cochlear implantation in children with CVM. Methods: Fifty-nine children with CVM who had used a cochlear implant for more than 3 years were included. CVM was classified into 4 subtypes based on the morphology of the cochlea and the modiolus on temporal bone computed tomography (TBCT): normal cochlea and normal modiolus (type A, n = 16), malformed cochlea and partial modiolus (type B, n = 31), malformed cochlea and no modiolus (type C, n = 6), and no cochlea and no modiolus (type D, n = 6). Speech perception test scores were compared between the subtypes of CVM using analysis of covariance with post hoc Bonferroni test. Univariate and multivariate regression analyses were used to identify the significant predictors of the speech perception test scores. Results: The speech perception test scores after implantation were significantly better in children with CVM type A or type B than in children with CVM type C or type D. The test scores did not differ significantly between the implanted children with CVM type A or type B and those without CVM. In univariate regression analysis, the type of CVM was a significant predictor of the speech perception test scores in implanted children with CVM. Multivariate regression analysis revealed that the age at cochlear implantation, cochlear nerve size and preimplantation speech perception test scores were significant predictors of the postimplantation speech perception test scores. The chance of cochlear nerve deficiency increased progressively from CVM type A to type D. Conclusion: The new classification of CVM based on the morphology of the cochlea and the modiolus is simple and easy to use, and correlated well with postimplantation speech perception ability and cochlear nerve status. This simple classification of CVM using TBCT with cochlear nerve assessment by magnetic resonance imaging is helpful in the preoperative evaluation of children with CVM.

ROOT SYSTEMS ARISING FROM AUTOMORPHISMS

2012 ◽  
Vol 11 (03) ◽  
pp. 1250057 ◽  
Author(s):  
SAEID AZAM ◽  
MALIHE YOUSOSFZADEH
Keyword(s):  
Lie Algebras ◽  
Root Systems ◽  
Affine Lie Algebras ◽  
Combinatorial Approach ◽  
Reflection Algebras ◽  
Affine Root Systems ◽  
Outstanding Work ◽  
Affine Reflection

We study a combinatorial approach of producing new root systems from the old ones in the context of affine root systems and their new generalizations. The appearance of this approach in the literature goes back to the outstanding work of Kac in the realization of affine Kac–Moody Lie algebras. In recent years, this approach has been appeared in many other works, including the study of affinization of extended affine Lie algebras and invariant affine reflection algebras.

A New Class of Representations of EALA Coordinated by Quantum Tori in Two Variables

2002 ◽  
Vol 45 (4) ◽  
pp. 672-685 ◽  
Author(s):  
S. Eswara Rao ◽  
Punita Batra
Keyword(s):  
Lie Algebras ◽  
Primitive Root ◽  
Irreducible Module ◽  
Affine Lie Algebras ◽  
Quantum Torus ◽  
New Class ◽  
Root Of Unity ◽  
Quantum Tori ◽  
Finite Dimensional

AbstractWe study the representations of extended affine Lie algebras where q is N-th primitive root of unity (ℂq is the quantum torus in two variables). We first prove that ⊕ for a suitable number of copies is a quotient of . Thus any finite dimensional irreducible module for ⊕ lifts to a representation of . Conversely, we prove that any finite dimensional irreducible module for comes from above. We then construct modules for the extended affine Lie algebras which is integrable and has finite dimensional weight spaces.

scholarly journals A BIOLOGICAL CLASSIFICATION OF ENCAPSULATUS PNEUMONIÆ (FRIEDLÄNDER'S BACILLUS)

1926 ◽  
Vol 44 (1) ◽  
pp. 113-128 ◽  
Author(s):  
Louis A. Julianelle
Keyword(s):  
Serological Test ◽  
Type A ◽  
Heterogeneous Group ◽  
Type B ◽  
Biological Classification ◽  
Type C ◽  
Working Out

A biological classification has been made of thirty strains of Friedländer's bacillus. This study reveals that there exist among these strains three sharply defined and specific types and one heterogeneous group. The three types are Type A, fifteen strains; Type B, six strains; Type C, three strains; and Group X, six strains. The agglutination, agglutinin adsorption, protection, thread, and precipitin reactions have been employed in the working out of this classification, and the types have been proved highly specific by means of each serological test.

Generalized Reductive Lie Algebras: Connections With Extended Affine Lie Algebras and Lie Tori

2006 ◽  
Vol 58 (2) ◽  
pp. 225-248 ◽  
Author(s):  
Saeid Azam
Keyword(s):  
Fixed Point ◽  
Root System ◽  
Lie Algebra ◽  
Lie Algebras ◽  
Affine Lie Algebras ◽  
The Core ◽  
Direct Sum ◽  
Reductive Lie Algebra ◽  
Intensive Investigation

AbstractWe investigate a class of Lie algebras which we call generalized reductive Lie algebras. These are generalizations of semi-simple, reductive, and affine Kac–Moody Lie algebras. A generalized reductive Lie algebra which has an irreducible root system is said to be irreducible and we note that this class of algebras has been under intensive investigation in recent years. They have also been called extended affine Lie algebras. The larger class of generalized reductive Lie algebras has not been so intensively investigated. We study themin this paper and note that one way they arise is as fixed point subalgebras of finite order automorphisms. We show that the core modulo the center of a generalized reductive Lie algebra is a direct sum of centerless Lie tori. Therefore one can use the results known about the classification of centerless Lie tori to classify the cores modulo centers of generalized reductive Lie algebras.

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