Related papers: A Scientific Biography of Cahit Arf (1910-1997)

Cem Tezer was a fastidious, meticulous, highly idiosyncratic and versatile scientist. Without him Turkish community of mathematics would be incomplete. Our sense of gratitude for his work in various areas of mathematics, history of…

We use categorical description of the invariant 2-cohomology group of Hopf algebra to compute such cohomology for two finite dimensional Hopf algebras: the group ring of $Z_8\rtimes Aut(Z_8)$ and Kac-Paljutkin algebra. For the first of…

In this thesis we consider two constructions generalizing the classical Arf invariant. In the first construction an $\epsilon$-symmetric quadratic form over a ring with involution $R$ is lifted to an $\epsilon(1+T)$-symmetric quadratic form…

In remembrance of Professor Uffe Valentin Haagerup (1949--2015), as a brilliant mathematician, we review some aspects of his life, and his outstanding mathematical accomplishments.

Extending results of Rais-Tauvel, Macedo-Savage, and Arakawa-Premet, we prove that under mild restrictions on the Lie algebra $\mathfrak q$ having the polynomial ring of symmetric invariants, the m-th Takiff algebra of $\mathfrak q$,…

This is a survey of results that extend notions of the classical invariant theory of linear actions by finite groups on $k[x_1, \dots, x_n]$ to the setting of finite group or Hopf algebra $H$ actions on an Artin-Schelter regular algebra…

This paper extends classical results in the invariant theory of finite groups and finite group schemes to the actions of finite Hopf algebras on commutative rings.

In the paper, the representation rings (or the Green rings) for a family of Hopf algebras of tame type, the 2-rank Taft algebra (at $q=-1$) and its two relatives twisted by 2-cocycles are explicitly described via a representation theoretic…

For a given finite dimensional Hopf algebra $H$ we describe the set of all equivalence classes of cocycle deformations of $H$ as an affine variety, using methods of geometric invariant theory. We show how our results specialize to the…

We study algebraic properties of Hopf group-coalgebras, recently introduced by Turaev. We show the existence of integrals and traces for such coalgebras, and we generalize the main properties of quasitriangular and ribbon Hopf algebras to…

This manuscript synthesizes almost fifteen years of research in algebraic combinatorics, in order to highlight, theme by theme, its perspectives. In part one, building on my thesis work, I use tools from commutative algebra, and in…

An alternative construction, using Witt's formalism, of the Arf-invariant of quadratic forms in characteristic 2.

Detlef D\"urr (1951-2021) was a theoretical and mathematical physicist who worked particularly on the foundations of quantum mechanics, electromagnetism, and statistical mechanics. This piece is a rather personal look back at him and his…

We generalize a result of Araki (1985) on indecomposable group representations with invariant (necessarily indefinite) inner product and irreducible subrepresentation to Hopf $*$-algebras. Moreover, we characterize invariant inner products…

This is a survey article on the invariant rings of Hopf actions

Inequalities play important roles not only in mathematics, but also in other fields, such as economics and engineering. Even though many results are published on Hermite-Hadamard (H-H) type inequalities, new researcher to this fields often…

The algebraic structures known as {\it Leavitt path algebras} were initially developed in 2004 by Ara, Moreno and Pardo, and almost simultaneously (using a different approach) by the author and Aranda Pino. During the intervening decade,…

We give an a geometric interpretation of the Hasse-Arf theorem for function fields using the recently proved Oort conjecture.

The analytical aspects of the "Trait\'e des \'equations" of Sharaf al-D\^in al-T\^us\^i (2nd half of the XIIth century) have been underlined by R. Rashed (1974, 1986). In the present paper, we consider again some of those aspects, when…

Classical random walks and Markov processes are easily described by Hopf algebras. It is also known that groups and Hopf algebras (quantum groups) lead to classical and quantum diffusions. We study here the more primitive notion of a…