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Remarks on Isomorphisms of Simple Inductive Types

2003
*
Electronical Notes in Theoretical Computer Science
*

¼¹

doi:10.1016/s1571-0661(04)80760-6
fatcat:tvaolt4a3jcthilbuml7k42ft4
*ÖÑ*ÒØ ÑÔÐ ×*ÖÑ*ÒØº 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×º Ò Ø ÓÒ ¾º Ì × Ø Ó Ø*ÖÑ*× × Ò Ö Ø Ý Ø ÓÐÐÓÛ Ò Ö ÑÑ Ö ÖÙÐ Å Ü ´ Ü ¡ Åµ ´Å Åµ 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 ...##
###
A Linear Logical View of Linear Type Isomorphisms
[chapter]

1999
*
Lecture Notes in Computer Science
*

In this paper we give a

doi:10.1007/3-540-48168-0_18
fatcat:xrxkgtwk3ffrxfyr75mben2c5m
*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. ...##
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On the number of inductively minimal geometries

2001
*
Theoretical Computer Science
*

We count the number

doi:10.1016/s0304-3975(00)00228-0
fatcat:wkck4w7ydrdk3ifcxwhvzz7gui
*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. ...##
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A simple separable C*-algebra not isomorphic to its opposite algebra

2004
*
Proceedings of the American Mathematical Society
*

We give an example

doi:10.1090/s0002-9939-04-07330-7
fatcat:rpgkb6keizavdmnsu3iqozcj4e
*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. ...##
###
Artin rings of global dimension two

1985
*
Journal of Algebra
*

In this paper, we show that a left artin ring A

doi:10.1016/0021-8693(85)90127-9
fatcat:bbhomkrwuvdixdthvfo27umwxm
*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. ...##
###
SimpleC*-algebra generated by isometries

1977
*
Communications in Mathematical Physics
*

As a consequence we show that G n is

doi:10.1007/bf01625776
fatcat:zgmuxdp46bhjlakxtxg4pwrb2e
*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. ...##
###
A simple separable C*-algebra not isomorphic to its opposite algebra
[article]

2002
*
arXiv
*
pre-print

We give an example

arXiv:math/0208084v1
fatcat:wkpsgxfcvjekbh2evhdumz7h3i
*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. ...##
###
A geometric proof of the conjugacy of borel and Cartan subalgebras of the classical simple Lie algebras

1980
*
Advances in Mathematics
*

L is

doi:10.1016/0001-8708(80)90025-0
fatcat:jj65ew4aqjc7diazz5opuae5x4
*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. ...##
###
On the classification of inductive limits of sequences of semisimple finite-dimensional algebras

1976
*
Journal of Algebra
*

algebra, and determines the

doi:10.1016/0021-8693(76)90242-8
fatcat:am6efkdlavaedmj2muhsisvul4
*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. ...##
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Category decomposition of Rep_k(SL_n(F))
[article]

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 ...

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

2018
*
arXiv
*
pre-print

We prove the uniqueness

arXiv:1803.01385v1
fatcat:fc2j3wa7vbf6vlpkuvh4iohm5q
*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. ...##
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Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal

2020
*
Discrete Mathematics & Theoretical Computer Science
*

The nodes

doi:10.46298/dmtcs.6388
fatcat:mdydcpx7k5fp3jlpy5l5lh46bm
*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 . ...##
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Moduli of simple holomorphic pairs and effective divisors

2000
*
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
*

In this note we identify two complex structures (

doi:10.1007/bf02940918
fatcat:ncm4kjeosrapdjzhoroxh5vn4q
*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. ...##
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Blocks with a cyclic defect group

1975
*
Journal of Algebra
*

So as j c;t / < / Nt j we may apply

doi:10.1016/0021-8693(75)90181-7
fatcat:lpbdgvhtendgfo4ln3x3lcqgju
*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*. ...##
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Some remarks on the center of the universal enveloping algebra of a classical simple Lie algebra

1976
*
Pacific Journal of Mathematics
*

As before

doi:10.2140/pjm.1976.62.93
fatcat:j6d3gb73w5bmvf3mqkdwhtnwky
*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? ...
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