ON THE EQUATIONAL THEORY OF PROJECTION LATTICES OF FINITE VON NEUMANN FACTORS

被引：10

作者：

Herrmann, Christian ^{[1
]}

机构：

[1] Tech Univ Darmstadt, FB Math, D-64289 Darmstadt, Germany

来源：

JOURNAL OF SYMBOLIC LOGIC | 2010年 / 75卷 / 03期

关键词：

von Neumann algebra; projection lattice; continuous geometry; equational theory; MODULAR LATTICES; WORD PROBLEMS; ALGEBRA; LOGIC; RING;

D O I：

10.2178/jsl/1278682219

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For a finite von Neumann algebra factor M. the projections form a modular ortholattice L(M). We show that the equational theory of L(M) coincides with that of some resp. all L(C(nxn)) and is decidable. In contrast, the uniform word problem for the variety generated by all L(C(nxn)) is shown to be undecidable.

引用

页码：1102 / 1110

页数：9

共 50 条

[11] On automorphisms of finite von Neumann algebras leaving invariant some reflexive lattices
Wu, Wenming
Yuan, Wei
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2017, 49 (03) : 369 - 379
[12] Wigner distributions on von Neumann lattices
Zak, J
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1999, 32 (25): : 4787 - 4794
[13] On function lattices and commutative von Neumann algebras
Edwards, DA
QUARTERLY JOURNAL OF MATHEMATICS, 2002, 53 : 19 - 29
[14] Orthonormal coherent states on von Neumann lattices
Zak, J
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (05): : 1063 - 1069
[15] LOGICALLY INDEPENDENT VON-NEUMANN LATTICES
REDEI, M
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS, 1995, 34 (08) : 1711 - 1718
[16] THE LOGARITHMIC FUNCTION AND TRACE ZERO ELEMENTS IN FINITE VON NEUMANN FACTORS
Molnar, Lajos
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2016, 94 (02) : 290 - 295
[17] ON REDUCTION THEORY OF VON NEUMANN
SAKAI, S
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1964, 70 (03) : 393 - &
[18] The ring of an outer von Neumann frame in modular lattices
Czedli, Gabor
Skublics, Benedek
ALGEBRA UNIVERSALIS, 2010, 64 (1-2) : 187 - 202
[19] Generalized Bargmann functions, their growth and von Neumann lattices
Vourdas, A.
Penson, K. A.
Duchamp, G. H. E.
Solomon, A. I.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2012, 45 (24)
[20] Wilson-like functions on von Neumann lattices
Zak, J
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2002, 35 (26): : L369 - L375

← 1 2 3 4 5 →