Geodesic
Involutions in algebras of upper-triangular matrices
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2023), pp. 11-30.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we classify up to equivalency involutions of first kind in algebras of upper-triangular matrices over commutative rings. In case of a field $F$ of characteristics $2$ we obtain necessary and sufficient conditions for finiteness of the set of invlolutions equivalency classes of $T_{n}(F)$.
Keywords: involution, equivalency of invloutions, algebra of upper-triangular matrices. 
@article{IVM_2023_6_a1,
     author = {I. A. Kulguskin and D. T. Tapkin},
     title = {Involutions in algebras of upper-triangular matrices},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {11--30},
     publisher = {mathdoc},
     number = {6},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_6_a1/}
}
TY  - JOUR
AU  - I. A. Kulguskin
AU  - D. T. Tapkin
TI  - Involutions in algebras of upper-triangular matrices
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2023
SP  - 11
EP  - 30
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2023_6_a1/
LA  - ru
ID  - IVM_2023_6_a1
ER  - 
%0 Journal Article
%A I. A. Kulguskin
%A D. T. Tapkin
%T Involutions in algebras of upper-triangular matrices
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2023
%P 11-30
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2023_6_a1/
%G ru
%F IVM_2023_6_a1
I. A. Kulguskin; D. T. Tapkin. Involutions in algebras of upper-triangular matrices. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2023), pp. 11-30. http://geodesic.mathdoc.fr/item/IVM_2023_6_a1/

[1] Albert A. A., Structure of algebras, Amer. Math. Soc. Colloquium Publ., 24, AMS, Providence, R.I., 1961 | MR

[2] Knus M. A., Merkurjev A., Rost M., Tignol J.-P., The Book of Involutions, Amer. Math. Soc. Colloquium Publ., 44, AMS, Providence, R.I., 1998 | DOI | MR | Zbl

[3] Jacobson N., Finite-Dimensional Division Algebras over Fields, Springer-Verlag, Berlin, 1996 | MR | Zbl

[4] Vincenzo O. M., Koshlukov P., Scala R., “Involutions for upper triangular matrix algebras”, Adv. Appl. Math., 37:4 (2006), 541–568 | DOI | MR | Zbl

[5] Krylov P. A., Norbosambuev Ts. D., “Avtomorfizmy algebr formalnykh matrits”, Sib. matem. zhurn., 59:5 (2018), 1116–1127 | MR | Zbl

[6] Krylov P. A., Tuganbaev A. A., “Gruppy avtomorfizmov kolets formalnykh matrits”, Itogi nauki i tekhn. Ser. Sovrem. matem. i ee pril. Temat. obz., 164, 2019, 96–124

[7] Krylov P. A., Tuganbaev A. A., Automorphisms of Formal Matrix Rings, 2022, arXiv: 2204.13332 | MR

[8] Spiegel E., “Involutions in incidence algebras”, Linear Algebra and Appl., 405:1 (2005), 155–162 | DOI | MR | Zbl

[9] Brusamarello R., Fornaroli É.Z., Santulo E. A.(Jr)., “Classification of Involutions on Incidence Algebras”, Commun. Algebra, 39:6 (2011), 1941–1955 | DOI | MR | Zbl

[10] Brusamarello R., Lewis D. W., “Automorphisms and involutions on incidence algebras”, Linear and Multilinear Algebra, 59:11 (2011), 1247–1267 | DOI | MR | Zbl

[11] Brusamarello R., Fornaroli É.Z., Santulo E. A.(Jr)., “Anti-automorphisms and involutions on $($finitary$)$ incidence algebras”, Linear and Multilinear Algebra, 60:2 (2012), 181–188 | DOI | MR | Zbl

[12] Fornaroli E. Z., Pezzott R. E.M., “Anti-isomorphisms and involutions on the idealization of the incidence space over the finitary incidence algebra”, Linear Algebra Appl., 637:5 (2022), 82–109 | DOI | MR | Zbl

[13] Kezlan T. P., “A note on algebra automorphisms of triangular matrices over commutative rings”, Linear Algebra Appl., 135 (1990), 181—184 | DOI | MR | Zbl