4 problems

Antisymmetrized Euler form conjecture. The form $\langle\,,\,\rangle_a$ descends to the Grothendieck group $\operatorname{G_0}(\operatorname{mod} A_T)$, and its matrix in the basis…

Let $A$ be a tilted algebra. Its first Hochschild cohomology space is denoted by $H^1(A)$. Simply connectedness conjecture. The algebra $A$ is simply connected if and only if … Thi…

Igusa–Todorov's conjecture. There exists a tilted algebra $B$ such that $\Lambda\cong B\ltimes \operatorname{Ext}^2_B(DB,B)$ and the number of isomorphism classes of indecomposable…

Let $C$ be a tilted algebra, and let $E=\operatorname{Ext}_{C}^{2}(DC,C)$. Regard $E$ as a $C$-$C$-bimodule and decompose it into indecomposable summands. Orthogonality conjecture.…