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Involutive gradings of JBW-triple factors
Let ( B + , B − ) be an involutive grading of a JBW * -triple factor A with associated involutive triple automorphism φ . When the JBW * -subtriple B + of A is not a JBW * -triple factor there exists a non-zero Peirce weak * -closed inner ideal J in A with Peirce spaces J 0 , J 1 , and J 2 such that...
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| Published in: | Revista matemática complutense 2010-07, Vol.23 (2), p.383-413 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| container_end_page | 413 |
| container_issue | 2 |
| container_start_page | 383 |
| container_title | Revista matemática complutense |
| container_volume | 23 |
| creator | Edwards, C. Martin Morton, Alastair G. |
| description | Let (
B
+
,
B
−
) be an involutive grading of a JBW
*
-triple factor
A
with associated involutive triple automorphism
φ
. When the JBW
*
-subtriple
B
+
of
A
is not a JBW
*
-triple factor there exists a non-zero Peirce weak
*
-closed inner ideal
J
in
A
with Peirce spaces
J
0
,
J
1
, and
J
2
such that
When both
B
+
and
B
−
are JBW
*
-triple factors it is shown that either the situation reduces to that above with
J
0
or
J
2
equal to zero or, in the case that
B
+
(or, by symmetry,
B
−
) contains a unitary tripotent
v
, that
v
is unitary in
A
, and
where
H
(
A
2
(
v
),
φ
) is the JBW
*
-algebra of
φ
-invariant elements in the JBW
*
-algebra
A
2
(
v
), and
S
(
A
2
(
v
),
φ
) is the JBW
*
-triple of −
φ
-invariant elements of
A
2
(
v
). In the special case in which
A
is a discrete W
*
-factor it is shown that such a unitary tripotent always exists in
B
+
(or
B
−
), thereby completing the description of involutive gradings in this case. |
| doi_str_mv | 10.1007/s13163-009-0021-z |
| format | article |
| fullrecord | <record><control><sourceid>crossref_sprin</sourceid><recordid>TN_cdi_crossref_primary_10_1007_s13163_009_0021_z</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>10_1007_s13163_009_0021_z</sourcerecordid><originalsourceid>FETCH-LOGICAL-c240t-6f02acf2010113f61458f5a60ae98a1cbe256b45064601e27d221cab3f7d2f3e3</originalsourceid><addsrcrecordid>eNp9jz9PwzAQxS0EEqXwAdiyMhju_C_OCBWUokosIEbLce0oVUgqO61EPz2uwsxwd2-4d-9-hNwi3CNA-ZCQo-IUoMrFkB7PyAwrrSnTUJ5njbyiuelLcpXSFkBWQosZuVv1h6Hbj-3BF020m7ZvUjGE4u3pi46x3XW-CNaNQ0zX5CLYLvmbvzknny_PH4tXun5frhaPa-qYgJGqAMy6wAAhxwWFQuogrQLrK23R1Z5JVQsJSihAz8oNY-hszUNWgXs-JzjddXFIKfpgdrH9tvHHIJgTq5lYTWY1J1ZzzB42eVLe7RsfzXbYxz6_-Y_pF6IIVkc</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Involutive gradings of JBW-triple factors</title><source>Springer Nature</source><creator>Edwards, C. Martin ; Morton, Alastair G.</creator><creatorcontrib>Edwards, C. Martin ; Morton, Alastair G.</creatorcontrib><description>Let (
B
+
,
B
−
) be an involutive grading of a JBW
*
-triple factor
A
with associated involutive triple automorphism
φ
. When the JBW
*
-subtriple
B
+
of
A
is not a JBW
*
-triple factor there exists a non-zero Peirce weak
*
-closed inner ideal
J
in
A
with Peirce spaces
J
0
,
J
1
, and
J
2
such that
When both
B
+
and
B
−
are JBW
*
-triple factors it is shown that either the situation reduces to that above with
J
0
or
J
2
equal to zero or, in the case that
B
+
(or, by symmetry,
B
−
) contains a unitary tripotent
v
, that
v
is unitary in
A
, and
where
H
(
A
2
(
v
),
φ
) is the JBW
*
-algebra of
φ
-invariant elements in the JBW
*
-algebra
A
2
(
v
), and
S
(
A
2
(
v
),
φ
) is the JBW
*
-triple of −
φ
-invariant elements of
A
2
(
v
). In the special case in which
A
is a discrete W
*
-factor it is shown that such a unitary tripotent always exists in
B
+
(or
B
−
), thereby completing the description of involutive gradings in this case.</description><identifier>ISSN: 1139-1138</identifier><identifier>EISSN: 1988-2807</identifier><identifier>DOI: 10.1007/s13163-009-0021-z</identifier><language>eng</language><publisher>Milan: Springer Milan</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Geometry ; Mathematics ; Mathematics and Statistics ; Topology</subject><ispartof>Revista matemática complutense, 2010-07, Vol.23 (2), p.383-413</ispartof><rights>Revista Matemática Complutense 2009</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c240t-6f02acf2010113f61458f5a60ae98a1cbe256b45064601e27d221cab3f7d2f3e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Edwards, C. Martin</creatorcontrib><creatorcontrib>Morton, Alastair G.</creatorcontrib><title>Involutive gradings of JBW-triple factors</title><title>Revista matemática complutense</title><addtitle>Rev Mat Complut</addtitle><description>Let (
B
+
,
B
−
) be an involutive grading of a JBW
*
-triple factor
A
with associated involutive triple automorphism
φ
. When the JBW
*
-subtriple
B
+
of
A
is not a JBW
*
-triple factor there exists a non-zero Peirce weak
*
-closed inner ideal
J
in
A
with Peirce spaces
J
0
,
J
1
, and
J
2
such that
When both
B
+
and
B
−
are JBW
*
-triple factors it is shown that either the situation reduces to that above with
J
0
or
J
2
equal to zero or, in the case that
B
+
(or, by symmetry,
B
−
) contains a unitary tripotent
v
, that
v
is unitary in
A
, and
where
H
(
A
2
(
v
),
φ
) is the JBW
*
-algebra of
φ
-invariant elements in the JBW
*
-algebra
A
2
(
v
), and
S
(
A
2
(
v
),
φ
) is the JBW
*
-triple of −
φ
-invariant elements of
A
2
(
v
). In the special case in which
A
is a discrete W
*
-factor it is shown that such a unitary tripotent always exists in
B
+
(or
B
−
), thereby completing the description of involutive gradings in this case.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Geometry</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Topology</subject><issn>1139-1138</issn><issn>1988-2807</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2010</creationdate><recordtype>article</recordtype><recordid>eNp9jz9PwzAQxS0EEqXwAdiyMhju_C_OCBWUokosIEbLce0oVUgqO61EPz2uwsxwd2-4d-9-hNwi3CNA-ZCQo-IUoMrFkB7PyAwrrSnTUJ5njbyiuelLcpXSFkBWQosZuVv1h6Hbj-3BF020m7ZvUjGE4u3pi46x3XW-CNaNQ0zX5CLYLvmbvzknny_PH4tXun5frhaPa-qYgJGqAMy6wAAhxwWFQuogrQLrK23R1Z5JVQsJSihAz8oNY-hszUNWgXs-JzjddXFIKfpgdrH9tvHHIJgTq5lYTWY1J1ZzzB42eVLe7RsfzXbYxz6_-Y_pF6IIVkc</recordid><startdate>20100701</startdate><enddate>20100701</enddate><creator>Edwards, C. Martin</creator><creator>Morton, Alastair G.</creator><general>Springer Milan</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20100701</creationdate><title>Involutive gradings of JBW-triple factors</title><author>Edwards, C. Martin ; Morton, Alastair G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c240t-6f02acf2010113f61458f5a60ae98a1cbe256b45064601e27d221cab3f7d2f3e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2010</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Geometry</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Edwards, C. Martin</creatorcontrib><creatorcontrib>Morton, Alastair G.</creatorcontrib><collection>CrossRef</collection><jtitle>Revista matemática complutense</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Edwards, C. Martin</au><au>Morton, Alastair G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Involutive gradings of JBW-triple factors</atitle><jtitle>Revista matemática complutense</jtitle><stitle>Rev Mat Complut</stitle><date>2010-07-01</date><risdate>2010</risdate><volume>23</volume><issue>2</issue><spage>383</spage><epage>413</epage><pages>383-413</pages><issn>1139-1138</issn><eissn>1988-2807</eissn><abstract>Let (
B
+
,
B
−
) be an involutive grading of a JBW
*
-triple factor
A
with associated involutive triple automorphism
φ
. When the JBW
*
-subtriple
B
+
of
A
is not a JBW
*
-triple factor there exists a non-zero Peirce weak
*
-closed inner ideal
J
in
A
with Peirce spaces
J
0
,
J
1
, and
J
2
such that
When both
B
+
and
B
−
are JBW
*
-triple factors it is shown that either the situation reduces to that above with
J
0
or
J
2
equal to zero or, in the case that
B
+
(or, by symmetry,
B
−
) contains a unitary tripotent
v
, that
v
is unitary in
A
, and
where
H
(
A
2
(
v
),
φ
) is the JBW
*
-algebra of
φ
-invariant elements in the JBW
*
-algebra
A
2
(
v
), and
S
(
A
2
(
v
),
φ
) is the JBW
*
-triple of −
φ
-invariant elements of
A
2
(
v
). In the special case in which
A
is a discrete W
*
-factor it is shown that such a unitary tripotent always exists in
B
+
(or
B
−
), thereby completing the description of involutive gradings in this case.</abstract><cop>Milan</cop><pub>Springer Milan</pub><doi>10.1007/s13163-009-0021-z</doi><tpages>31</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1139-1138 |
| ispartof | Revista matemática complutense, 2010-07, Vol.23 (2), p.383-413 |
| issn | 1139-1138 1988-2807 |
| language | eng |
| recordid | cdi_crossref_primary_10_1007_s13163_009_0021_z |
| source | Springer Nature |
| subjects | Algebra Analysis Applications of Mathematics Geometry Mathematics Mathematics and Statistics Topology |
| title | Involutive gradings of JBW-triple factors |
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