Geodesic
$N$-homogeneous $C^*$-algebras generated by idempotents
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2011), pp. 94-103.

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In this paper we consider the $n$-homogeneous $C^*$-algebras generated by idempotents. We prove that a finitely generated unital $n$-homogeneous (when $n$ is greater than or equal to $2$) $C^*$-algebra $A$ can be generated by finite number of idempotents if and only if the algebra $A$ contains at least one non-trivial idempotent.
Keywords: $n$-homogeneous $C^*$-algebra, algebraic bundle, idempotent, finitely generated algebra. 
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M. V. Shchukin. $N$-homogeneous $C^*$-algebras generated by idempotents. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2011), pp. 94-103. http://geodesic.mathdoc.fr/item/IVM_2011_7_a9/

[1] Antonevich A., Krupnik N., “On trivial and non-trivial $n$-homogeneous $C^*$-algebras”, Integr. Equ. Oper. Theory, 38:2 (2000), 172–189 | DOI | MR | Zbl

[2] Davis C., “Generators of the ring of bounded operators”, Proc. Amer. Math. Soc., 6:6 (1955), 970–972 | DOI | MR | Zbl

[3] Krupnik N. Ya., Banakhovy algebry s simvolom i singulyarnye integralnye operatory, Shtiintsa, Kishinev, 1984 | MR | Zbl

[4] Krupnik N., Roch S., Silbermann B., “On $C^*$-algebras generated by idempotents”, J. Funct. Anal., 137:2 (1996), 303–319 | DOI | MR | Zbl

[5] Raeburn I., Sinclair A. M., “The $C^*$-algebra generated by two projections”, Math. Scand., 65:2 (1989), 278–290 | MR | Zbl

[6] Böttcher A., Gohberg I., Karlovich Yu., Krupnik N., Roch S., Silbermann B., Spitkovsky I., “Banach algebras generated by $n$ idempotents and applications”, Oper. Theory. Advances and Appl., 90 (1996), 19–54 | MR

[7] Ostrovskyi V., Samoilenko Yu., “Introduction to the theory of representations of finitely presented $*$-algebras. I: Representations by bounded operators”, Rev. Math. Math. Phys., 11:1 (1999), 1–261 | DOI | MR | Zbl

[8] Rabanovich S., Samoilenko Yu., “On representations of $F_n$-algebras and invertibility symbols”, Methods Funct. Anal. Topology, 4:4 (1998), 86–96 | MR | Zbl

[9] Roch S., Silbermann B., “Algebras generated by idempotents and the symbol calculus for singular integral operators”, Integr. Equat. Oper. Theory, 11:3 (1988), 385–419 | DOI | MR | Zbl

[10] Mischenko A. S., Vektornye rassloeniya i ikh primeneniya, Nauka, M., 1984 | MR

[11] Vasilev N. B., “$C^*$-algebry s konechnomernymi neprivodimymi predstavleniyami”, UMN, 21:1 (1966), 135–154 | MR | Zbl

[12] Kaplansky I., “The structure of certain operator algebras”, Trans. Amer. Math. Soc., 70:2 (1951), 219–255 | DOI | MR | Zbl

[13] Naimark M. A., Normirovannye koltsa, GITTL, M., 1956

[14] Schukin M. V., “Netrivialnaya $C^*$-algebra, porozhdennaya tremya idempotentami”, Izv. AH Belarusi. Fiz.-matem. ser., 2002, no. 4, 29–34