Was James the son of Alphaeus the presiding Apostle at the first Council held in Jerusalem?

I am reading The Upper Room by Bishop J.C. Ryle and I came to this passage that surprised me: > James the son of Alphaeus was there, who had the honour of being the > presiding Apostle at the first Council held in Jerusalem, and of whom > St. Paul tells the Galatians that, together with Peter and John, James > was a "pillar of the Church" (Gal. 2:9). Is that accurate? Was James the son of Alphaeus the presiding Apostle at the first Council held in Jerusalem? And if not, was he generally thought to have been in the 19th century (by evangelicals)?