JHEP06(2023)192 Published for SISSA by Springer Received: May 30, 2023 Accepted: May 31, 2023 Published: June 27, 2023 Erratum: Special Vinberg cones and the entropy of BPS extremal black holes Dmitri V. Alekseevsky, a,b Alessio Marrani c and Andrea Spiro d a Institute for Information Transmission Problems, B. Karetnuj per. 19, Moscow 127051, Russia b Faculty of Science, University of Hradec Králové, Rokitanského 62, Hradec Králové 500 03, Czech Republic c Centro Studi e Ricerche Enrico Fermi, via Panisperna 89A, Roma I-00184, Italy d Scuola di Scienze e Tecnologie, Università di Camerino, Via Madonna delle Carceri, Camerino I-62032, Macerata, Italy E-mail: dalekseevsky@iitp.ru, jazzphyzz@gmail.com, andrea.spiro@unicam.it Erratum to: JHEP11(2021)100 ArXiv ePrint: 2107.06797 In [1] and in [2] an error occured in the computations for the G 0 -invariant polynomials of degree 3 of the special Vinberg cones. As a consequence, it was erroneously stated that for any special Vinberg cone V, the G 0 -invariant homogeneous functions of degree 3 of V and its dual V ∗ are equal polynomials. A correct computation shows that only for the dual cone V ∗ the G 0 -invariant homogeneous function of degree 3 is a polynomial, while for V the corresponding function is a (non polynomial) rational function. Due to this, the statement of Thm. 3.2 in [2] is not correct. However this error is easily amended if the roles of V and its dual V ∗ are interchanged. Such a swap is immediately obtained if the definition of the special T -algebras is modified as follows ([2, Def. 2.1]): A 12 should be set equal to A 12 = S 0 (instead of A 12 = V ), A 23 should be set equal to A 23 = V (instead of A 23 = S 0 ) and the product between s 0 ∈ A 12 and v ∈ A 23 should be set equal to s 0 ·v := µ(v,s 0 ) (instead of the previous rule given by v·s 0 := µ(v,s 0 )). If this new definition is applied throughout the paper, basically all statements and proofs of [2] (and, in particular, Thm 3.2) become fully correct. The only side effects of this change is that new corrective terms appear in certain explicit formulas. More precisely: Open Access,c ⃝ The Authors. Article funded by SCOAP 3 . https://doi.org/10.1007/JHEP06(2023)192