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Remarks on Isomorphisms of Simple Inductive Types

David Chemouil, Sergei Soloviev
2003 Electronical Notes in Theoretical Computer Science  
¼¹ ÖÑ ÒØ ÑÔÐ × ÖÑ Òغ ¾ Ê Ñ Ö ¿º Ë Ò Ø ×Ù Ñ ×× ÓÒ Ó Ø × Ô Ô Ö¸Û ÓÙÒ ×ÓÑ Ö Ö Ò × ÓÙØ Û Ø Û ÐÐ ÖÑ ÒØ Ä ÑÑ ´ º ¾¸½ Ò ÑÓ×Ø ÒÓØ ÐÝ ½¾ µº Ï Ð Û × ÐÐ Ô ÐÐ Ò Ø × ÔÖÓÔ ÖØÝ ÖÑ ÒØ Ò Ø ÙÖÖ ÒØ Ô Ô ÖÛ ÒØ Ò ØÓ Ù× Ø ÔÖ  ...  × Ó Ø Ð Ò Ù º ¾º¾ Ì ÖÑ× Ï Û ÐÐ ÒÓÛ Ò Ø Ø ÖÑ× Ó ÓÙÖ Ð ÙÐÙ׺ Ò Ø ÓÒ ¾º Ì × Ø Ó Ø ÖÑ× × Ò Ö Ø Ý Ø ÓÐÐÓÛ Ò Ö ÑÑ Ö ÖÙÐ Å Ü ´ Ü ¡ ŵ ´Å ŵ Ê Û Ö Ü ¾ Î ¾ Ò Ò Ö ØÝÔ ×º AEÓØ ÔÔÐ Ø ÓÒ × Ð Ø¹ ××Ó Ø Ú ¸ Ò ´ ´Å ½ Å  ... 
doi:10.1016/s1571-0661(04)80760-6 fatcat:tvaolt4a3jcthilbuml7k42ft4

A Linear Logical View of Linear Type Isomorphisms [chapter]

Vincent Balat, Roberto Di Cosmo
1999 Lecture Notes in Computer Science  
In this paper we give a remarkably simple and elegant characterization of linear isomorphisms in the setting of Multiplicative Linear Logic (MLL), by making an essential use of the correctness criterion  ...  The notion of isomorphisms of types has many theoretical as well as practical consequences, and isomorphisms of types have been investigated at length over the past years.  ...  A first remark, which is important for a simple treatment of linear isomorphisms, is that we can focus, w.l.o.g., on witnesses of isomorphisms which are simple proof nets.  ... 
doi:10.1007/3-540-48168-0_18 fatcat:xrxkgtwk3ffrxfyr75mben2c5m

On the number of inductively minimal geometries

Philippe Cara, Serge Lehman, Dimitrii V. Pasechnik
2001 Theoretical Computer Science  
We count the number of inductively minimal geometries for any given rank by exhibiting a correspondence between the inductively minimal geometries of rank n and the trees with n + 1 vertices.  ...  The proof of this correspondence uses the van Rooij-Wilf characterization of line graphs (see [11] ).  ...  For each integer n¿1; there exists a one-to-one correspondence between the set of non-isomorphic inductively minimal geometries of rank n and the set of non-isomorphic trees with n + 1 vertices.  ... 
doi:10.1016/s0304-3975(00)00228-0 fatcat:wkck4w7ydrdk3ifcxwhvzz7gui

A simple separable C*-algebra not isomorphic to its opposite algebra

N. Christopher Phillips
2004 Proceedings of the American Mathematical Society  
We give an example of a simple separable C*-algebra that is not isomorphic to its opposite algebra.  ...  It has trivial K 1 , and its K 0 -group is order isomorphic to a countable subgroup of R.  ...  There exists a simple separable stably finite unital C* subalgebra A that is not isomorphic to the complexification of any real C*-algebra. Remark 4.2.  ... 
doi:10.1090/s0002-9939-04-07330-7 fatcat:rpgkb6keizavdmnsu3iqozcj4e

Artin rings of global dimension two

Edward L Green, William H Gustafson, Dan Zacharia
1985 Journal of Algebra  
In this paper, we show that a left artin ring A of global dimension at most two has Loewy length at most 2" -1, where n is the number of simple components of A/rad(A).  ...  The projective dimension over /i of X is written as pd,X; gl.dim. ,4 is the global dimension of A. The linear dimension of a k-vector space V is  ...  ProoJ: Again, we use induction on the number of isomorphism classes of simple left R-modules. As noted above, the case where this number is one is trivial.  ... 
doi:10.1016/0021-8693(85)90127-9 fatcat:bbhomkrwuvdixdthvfo27umwxm

SimpleC*-algebra generated by isometries

Joachim Cuntz
1977 Communications in Mathematical Physics  
As a consequence we show that G n is simple and that its isomorphism type does not depend on the choice of S l9 ... 9 S n .  ...  While non-separable algebras of this type are well known (e.g. the Calkin algebra or type III factors on a separable Hubert space) there is to my knowledge no explicit example of a separable simple infinite  ...  Kadison and the members of the Department of Mathematics at the University of Pennsylvania, where the last part of this work has been completed.  ... 
doi:10.1007/bf01625776 fatcat:zgmuxdp46bhjlakxtxg4pwrb2e

A simple separable C*-algebra not isomorphic to its opposite algebra [article]

N. Christopher Phillips
2002 arXiv   pre-print
We give an example of a simple separable C*-algebra which is not isomorphic to its opposite algebra.  ...  It has trivial K_1, and its K_0-group is order isomorphic to a countable subgroup of the real numbers.  ...  There exists a simple separable stably finite unital C* subalgebra A which is not isomorphic to the complexification of any real C*-algebra. Remark 3.2.  ... 
arXiv:math/0208084v1 fatcat:wkpsgxfcvjekbh2evhdumz7h3i

A geometric proof of the conjugacy of borel and Cartan subalgebras of the classical simple Lie algebras

Michael A Gauger
1980 Advances in Mathematics  
L is simple of type B or D depending, respectively, on whether I' is odd or even-dimensional.  ...  We treat types B and D simultaneously and only a few remarks are needed to see that type C can be done nearly identically.  ... 
doi:10.1016/0001-8708(80)90025-0 fatcat:jj65ew4aqjc7diazz5opuae5x4

On the classification of inductive limits of sequences of semisimple finite-dimensional algebras

George A Elliott
1976 Journal of Algebra  
algebra, and determines the isomorphism type of the P-algebra.  ...  Hence the dimension group of an algebra which is the inductive limit of simple finite-dimensional algebras is of rank one. Conversely, every dimension group of rank one arises in this way.  ...  Since this subspace intersects the group only at zero, the ordered group is isomorphic, via the quotient map of R" by this subspace, to the subgroup (p f 4 tz j p, 4 ~2) of R with the relative order.  ... 
doi:10.1016/0021-8693(76)90242-8 fatcat:am6efkdlavaedmj2muhsisvul4

Category decomposition of Rep_k(SL_n(F)) [article]

Peiyi Cui
2021 arXiv   pre-print
of Rep_k(SL_n(F)).  ...  We establish a category decomposition of Rep_k(SL_n(F) according to the GL_n(F)-inertially equivalent supercuspidal classes of SL_n(F), and we give a block decomposition of the supercuspidal sub-category  ...  Let π be an irreducible supercuspidal k-representation of M, the above equivalence relation on maximal simple supercuspidal k-types induces an equivalence relation on I(π), which is the equivalence relation  ... 
arXiv:2110.03670v1 fatcat:fuxp6ltusvhfjc6kkh6xltxp4y

Vertex operator algebras generated by Ising vectors of σ-type [article]

Cuipo Jiang, Ching Hung Lam, Hiroshi Yamauchi
2018 arXiv   pre-print
We prove the uniqueness of the simple vertex operator algebra of OZ-type generated by Ising vectors of σ-type.  ...  We also prove that the simplicity can be omitted if the Griess algebra is isomorphic to the Matsuo algebra associated with the root system of type A_n.  ...  In this paper, we will prove the uniqueness of simple VOA structure of a VOA generated by Ising vectors of σ-type when it is of OZ-type, i.e., it is of CFT-type and the weight one subspace is trivial.  ... 
arXiv:1803.01385v1 fatcat:fc2j3wa7vbf6vlpkuvh4iohm5q

Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal

Henry Kvinge, Monica Vazirani
2020 Discrete Mathematics & Theoretical Computer Science  
The nodes of the fun-damental crystal correspond to simple modules of the corresponding cyclotomic KLR algebra.  ...  fundamental crystal, all in affine type.  ...  Set wt(M ) = −ν and wt i (M ) = − h i , ν . (13) Let Irr R be the set of isomorphism classes of simple R-modules and Irr R Λ be the set of isomorphism classes of simple modules in Rep Λ .  ... 
doi:10.46298/dmtcs.6388 fatcat:mdydcpx7k5fp3jlpy5l5lh46bm

Moduli of simple holomorphic pairs and effective divisors

Siegmund Kosarew, Paul Lupascu
2000 Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg  
In this note we identify two complex structures (one is given by algebraic geometry, the other by gauge theory) on the set of isomorphism classes of holomorphic bundles with section on a given compact  ...  In the case ofline bundles, these complex spaces are shown to be isomorphic to a space of effective divisors on the manifold  ...  The gauge-theoretical moduli space of simple holomorphic pairs of type E is analytically isomorphic to the complex-theoretical moduli space of simple holomorphic pairs of type E.  ... 
doi:10.1007/bf02940918 fatcat:ncm4kjeosrapdjzhoroxh5vn4q

Blocks with a cyclic defect group

R.M Peacock
1975 Journal of Algebra  
So as j c;t / < / Nt j we may apply induction and hence certainly deduce that & contains only one simple (up to isomorphism).But Dt 4 C, acts trivially on every simple in b,, , and so the simples in b,  ...  But D 4 C, acts trivially on every simple in b,, , and so the simples of &,r can be identified with the simples in b< . So up to isomorphism be, contains exactly one simple.  ... 
doi:10.1016/0021-8693(75)90181-7 fatcat:lpbdgvhtendgfo4ln3x3lcqgju

Some remarks on the center of the universal enveloping algebra of a classical simple Lie algebra

Michael A. Gauger
1976 Pacific Journal of Mathematics  
As before one sees p is onto and Z = K[z2 , --, z 2i ] where z 2k is as in(1).5. Simple algebras of typeD. Let L be simple of type D/.  ...  Simple algebras of type C.Let L be simple of type C,. Let V be a 2/-dimensional space with basis e1?  ... 
doi:10.2140/pjm.1976.62.93 fatcat:j6d3gb73w5bmvf3mqkdwhtnwky
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