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Solving the membership problem for parabolic Möbius monoids
For λ ∈ Q , λ > 0 , consider the submonoid S λ (resp. the subgroup G λ ) of S L 2 ( Q ) generated by two parabolic matrices A λ = 1 λ 0 1 and B λ = 1 0 λ 1 . We present new results and algorithms for the membership problem for the monoids S λ . For λ ∈ N ∗ , let us also consider the families of m...
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| Published in: | Semigroup forum 2019-06, Vol.98 (3), p.556-570, Article 556 |
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| Language: | English |
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| cites | cdi_FETCH-LOGICAL-c353t-c8873be11191930088bae03ff1665134ff4da05f6c07a850e89ffd109a7fa79d3 |
| container_end_page | 570 |
| container_issue | 3 |
| container_start_page | 556 |
| container_title | Semigroup forum |
| container_volume | 98 |
| creator | Esbelin, Henri-Alex Gutan, Marin |
| description | For
λ
∈
Q
,
λ
>
0
,
consider the submonoid
S
λ
(resp. the subgroup
G
λ
) of
S
L
2
(
Q
)
generated by two parabolic matrices
A
λ
=
1
λ
0
1
and
B
λ
=
1
0
λ
1
. We present new results and algorithms for the membership problem for the monoids
S
λ
. For
λ
∈
N
∗
,
let us also consider the families of monoids and subgroups of
S
L
2
(
Z
)
defined by
S
λ
=
1
+
λ
2
n
1
λ
n
2
λ
n
3
1
+
λ
2
n
4
∈
S
L
2
(
Z
)
∣
(
n
1
,
n
2
,
n
3
,
n
4
)
∈
N
4
,
G
λ
=
1
+
λ
2
n
1
λ
n
2
λ
n
3
1
+
λ
2
n
4
∈
S
L
2
(
Z
)
∣
(
n
1
,
n
2
,
n
3
,
n
4
)
∈
Z
4
.
Using continued fractions with partial quotients in
λ
N
,
we characterize the matrices of the monoid
S
λ
which belong to
S
λ
.
Our results are analogues for monoids of the classical result for groups of I. Sanov which says that
G
2
=
G
2
. |
| doi_str_mv | 10.1007/s00233-019-10013-4 |
| format | article |
| fullrecord | <record><control><sourceid>proquest_hal_p</sourceid><recordid>TN_cdi_hal_primary_oai_HAL_hal_02022620v1</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>2220800789</sourcerecordid><originalsourceid>FETCH-LOGICAL-c353t-c8873be11191930088bae03ff1665134ff4da05f6c07a850e89ffd109a7fa79d3</originalsourceid><addsrcrecordid>eNp9kMtKxDAUhoMoOI6-gKuCKxfRk6SXFNwMgzrCiAt1HdI2mWZom5p0BnwxX8AXM2NFwcWswgn_dy4fQucErghAdu0BKGMYSI5DTRiOD9CExIxiSlh2iCYALMMkJ_QYnXi_hlBDyibo5tk2W9OtoqFWUavaQjlfmz7qnS0a1UbauqiXTha2MWX0-PlRmI2PWttZU_lTdKRl49XZzztFr3e3L_MFXj7dP8xnS1yyhA245DxjhSIkzM8ZAOeFVMC0JmmaEBZrHVcSEp2WkEmegOK51hWBXGZaZnnFpuhy7FvLRvTOtNK9CyuNWMyWYvcHFChNKWxJyF6M2XDB20b5QaztxnVhPUEpBR5s8Tyk6JgqnfXeKf3bloDYGRWjURGMim-jIg4Q_weVZpCDsd3gpGn2o2xEfZjTrZT722oP9QXgvIlM</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>2220800789</pqid></control><display><type>article</type><title>Solving the membership problem for parabolic Möbius monoids</title><source>Springer Nature</source><creator>Esbelin, Henri-Alex ; Gutan, Marin</creator><creatorcontrib>Esbelin, Henri-Alex ; Gutan, Marin</creatorcontrib><description>For
λ
∈
Q
,
λ
>
0
,
consider the submonoid
S
λ
(resp. the subgroup
G
λ
) of
S
L
2
(
Q
)
generated by two parabolic matrices
A
λ
=
1
λ
0
1
and
B
λ
=
1
0
λ
1
. We present new results and algorithms for the membership problem for the monoids
S
λ
. For
λ
∈
N
∗
,
let us also consider the families of monoids and subgroups of
S
L
2
(
Z
)
defined by
S
λ
=
1
+
λ
2
n
1
λ
n
2
λ
n
3
1
+
λ
2
n
4
∈
S
L
2
(
Z
)
∣
(
n
1
,
n
2
,
n
3
,
n
4
)
∈
N
4
,
G
λ
=
1
+
λ
2
n
1
λ
n
2
λ
n
3
1
+
λ
2
n
4
∈
S
L
2
(
Z
)
∣
(
n
1
,
n
2
,
n
3
,
n
4
)
∈
Z
4
.
Using continued fractions with partial quotients in
λ
N
,
we characterize the matrices of the monoid
S
λ
which belong to
S
λ
.
Our results are analogues for monoids of the classical result for groups of I. Sanov which says that
G
2
=
G
2
.</description><identifier>ISSN: 0037-1912</identifier><identifier>EISSN: 1432-2137</identifier><identifier>DOI: 10.1007/s00233-019-10013-4</identifier><language>eng</language><publisher>New York: Springer US</publisher><subject>Algebra ; Algorithms ; Computer Science ; Discrete Mathematics ; Mathematics ; Mathematics and Statistics ; Monoids ; Quotients ; Research Article ; Subgroups</subject><ispartof>Semigroup forum, 2019-06, Vol.98 (3), p.556-570, Article 556</ispartof><rights>Springer Science+Business Media, LLC, part of Springer Nature 2019</rights><rights>Copyright Springer Nature B.V. 2019</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c353t-c8873be11191930088bae03ff1665134ff4da05f6c07a850e89ffd109a7fa79d3</citedby><cites>FETCH-LOGICAL-c353t-c8873be11191930088bae03ff1665134ff4da05f6c07a850e89ffd109a7fa79d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>230,314,776,780,881,27903,27904</link.rule.ids><backlink>$$Uhttps://uca.hal.science/hal-02022620$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Esbelin, Henri-Alex</creatorcontrib><creatorcontrib>Gutan, Marin</creatorcontrib><title>Solving the membership problem for parabolic Möbius monoids</title><title>Semigroup forum</title><addtitle>Semigroup Forum</addtitle><description>For
λ
∈
Q
,
λ
>
0
,
consider the submonoid
S
λ
(resp. the subgroup
G
λ
) of
S
L
2
(
Q
)
generated by two parabolic matrices
A
λ
=
1
λ
0
1
and
B
λ
=
1
0
λ
1
. We present new results and algorithms for the membership problem for the monoids
S
λ
. For
λ
∈
N
∗
,
let us also consider the families of monoids and subgroups of
S
L
2
(
Z
)
defined by
S
λ
=
1
+
λ
2
n
1
λ
n
2
λ
n
3
1
+
λ
2
n
4
∈
S
L
2
(
Z
)
∣
(
n
1
,
n
2
,
n
3
,
n
4
)
∈
N
4
,
G
λ
=
1
+
λ
2
n
1
λ
n
2
λ
n
3
1
+
λ
2
n
4
∈
S
L
2
(
Z
)
∣
(
n
1
,
n
2
,
n
3
,
n
4
)
∈
Z
4
.
Using continued fractions with partial quotients in
λ
N
,
we characterize the matrices of the monoid
S
λ
which belong to
S
λ
.
Our results are analogues for monoids of the classical result for groups of I. Sanov which says that
G
2
=
G
2
.</description><subject>Algebra</subject><subject>Algorithms</subject><subject>Computer Science</subject><subject>Discrete Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Monoids</subject><subject>Quotients</subject><subject>Research Article</subject><subject>Subgroups</subject><issn>0037-1912</issn><issn>1432-2137</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNp9kMtKxDAUhoMoOI6-gKuCKxfRk6SXFNwMgzrCiAt1HdI2mWZom5p0BnwxX8AXM2NFwcWswgn_dy4fQucErghAdu0BKGMYSI5DTRiOD9CExIxiSlh2iCYALMMkJ_QYnXi_hlBDyibo5tk2W9OtoqFWUavaQjlfmz7qnS0a1UbauqiXTha2MWX0-PlRmI2PWttZU_lTdKRl49XZzztFr3e3L_MFXj7dP8xnS1yyhA245DxjhSIkzM8ZAOeFVMC0JmmaEBZrHVcSEp2WkEmegOK51hWBXGZaZnnFpuhy7FvLRvTOtNK9CyuNWMyWYvcHFChNKWxJyF6M2XDB20b5QaztxnVhPUEpBR5s8Tyk6JgqnfXeKf3bloDYGRWjURGMim-jIg4Q_weVZpCDsd3gpGn2o2xEfZjTrZT722oP9QXgvIlM</recordid><startdate>20190615</startdate><enddate>20190615</enddate><creator>Esbelin, Henri-Alex</creator><creator>Gutan, Marin</creator><general>Springer US</general><general>Springer Nature B.V</general><general>Springer Verlag</general><scope>AAYXX</scope><scope>CITATION</scope><scope>1XC</scope></search><sort><creationdate>20190615</creationdate><title>Solving the membership problem for parabolic Möbius monoids</title><author>Esbelin, Henri-Alex ; Gutan, Marin</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c353t-c8873be11191930088bae03ff1665134ff4da05f6c07a850e89ffd109a7fa79d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Algebra</topic><topic>Algorithms</topic><topic>Computer Science</topic><topic>Discrete Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Monoids</topic><topic>Quotients</topic><topic>Research Article</topic><topic>Subgroups</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Esbelin, Henri-Alex</creatorcontrib><creatorcontrib>Gutan, Marin</creatorcontrib><collection>CrossRef</collection><collection>Hyper Article en Ligne (HAL)</collection><jtitle>Semigroup forum</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Esbelin, Henri-Alex</au><au>Gutan, Marin</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Solving the membership problem for parabolic Möbius monoids</atitle><jtitle>Semigroup forum</jtitle><stitle>Semigroup Forum</stitle><date>2019-06-15</date><risdate>2019</risdate><volume>98</volume><issue>3</issue><spage>556</spage><epage>570</epage><pages>556-570</pages><artnum>556</artnum><issn>0037-1912</issn><eissn>1432-2137</eissn><abstract>For
λ
∈
Q
,
λ
>
0
,
consider the submonoid
S
λ
(resp. the subgroup
G
λ
) of
S
L
2
(
Q
)
generated by two parabolic matrices
A
λ
=
1
λ
0
1
and
B
λ
=
1
0
λ
1
. We present new results and algorithms for the membership problem for the monoids
S
λ
. For
λ
∈
N
∗
,
let us also consider the families of monoids and subgroups of
S
L
2
(
Z
)
defined by
S
λ
=
1
+
λ
2
n
1
λ
n
2
λ
n
3
1
+
λ
2
n
4
∈
S
L
2
(
Z
)
∣
(
n
1
,
n
2
,
n
3
,
n
4
)
∈
N
4
,
G
λ
=
1
+
λ
2
n
1
λ
n
2
λ
n
3
1
+
λ
2
n
4
∈
S
L
2
(
Z
)
∣
(
n
1
,
n
2
,
n
3
,
n
4
)
∈
Z
4
.
Using continued fractions with partial quotients in
λ
N
,
we characterize the matrices of the monoid
S
λ
which belong to
S
λ
.
Our results are analogues for monoids of the classical result for groups of I. Sanov which says that
G
2
=
G
2
.</abstract><cop>New York</cop><pub>Springer US</pub><doi>10.1007/s00233-019-10013-4</doi><tpages>15</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0037-1912 |
| ispartof | Semigroup forum, 2019-06, Vol.98 (3), p.556-570, Article 556 |
| issn | 0037-1912 1432-2137 |
| language | eng |
| recordid | cdi_hal_primary_oai_HAL_hal_02022620v1 |
| source | Springer Nature |
| subjects | Algebra Algorithms Computer Science Discrete Mathematics Mathematics Mathematics and Statistics Monoids Quotients Research Article Subgroups |
| title | Solving the membership problem for parabolic Möbius monoids |
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